![]() ![]() ![]() ![]() FreshBooks co-founder Mike McDerment breaks down the objective of value-based pricing nicely in his e-book Breaking the Time Barrier: If you can sell based on value you can make much more money than if you’re using a cost-based model. Value-based pricing is both a selling technique and a pricing model. There is a reason cost-based pricing is the standard-it’s transparent and allows for greater accountability between designer and client. The hourly rate is determined by a number of factors: the size of the design shop, overhead costs, market demand, employees’ salaries, vacation and sick days, marketing objectives, and so on. It’s also called cost-plus pricing: “cost” meaning time and materials and “plus” meaning profit. In the custom web design industry, trading money for time is the standard. But it’s not the only way…Ĭost-based pricing means getting paid on time and materials-an hourly rate plus expenses. Looking at revenue growth and long term value to the client is one way to maximize profitability of your consulting or design work. The Westinghouse logo design by Paul Rand is rumored to have sold for $100,000. There are many cases of successful value-based pricing. For example, if website redesign for an ecommerce site has the potential of creating $1 million in additional revenue, a designer could price that redesign at 10% of its value, or $100,000. The idea is to frame the project as an investment in future value. Value-based pricing is a selling approach where you sell a project based on its value to the client. Let’s start by defining what value-based pricing and cost-based pricing mean. Hopefully this outline can guide you to make the best choice for your business. There are pros and cons to each method, and what’s worked for us in the past may not be the best decision for you. Pricing based on cost (time and materials).There are a couple approaches you can take that we’re going to review: With the expansion of eCommerce and Big Data, this last monitoring factor can be seen as a downside if it is not carried out properly.Whether you’re taking the plunge into freelancing and consulting or running a studio, there is one question that always looms over you: how am I going to price my services? This is one of the questions I’ve answered more than almost anything else over the years. It is important for companies to keep their production costs in mind, as well as managing the time they spend monitoring competitors and the prices set by them. The more you know about your rivals and what they are doing, the better you can decide how to manage your prices. Keeping an eye on existing and emerging competition by using a competitor website price monitoring software will allow you to be more competitive. Consequently, competitors may need to price their products lower or risk losing potential sales. In highly competitive markets, consumers judge products with similar features by the prices. This pricing method is normally used by businesses selling similar products, since services can vary from business to business, while the attributes of a product remain similar. It might forget about existing competitors.Ĭompetition-based pricing, also known as competitive pricing, consists in setting the price of a product based on what the competition is charging.Many companies mass-producing goods such as textiles, food and building materials use this pricing technique. The ideal thing to do, would be setting a price in between the floor and the ceiling. The floor and the ceiling are the minimum and maximum prices for a specific product or service – the price range. In this short guide we approach the three major and most common pricing strategies:Ĭost-based pricing strategies uses production costs as its basis for pricing and, to this base cost, a profit level must be added in order to come up with the product price.Ĭost-based pricing companies use their costs to find a price floor and a price ceiling. Let’s have a look at the most common pricing strategies. The right price can generate more sales while the wrong one can make potential customers look elsewhere. Price setting is part of the marketing process and it requires an in-depth market reasearch. ![]()
0 Comments
![]() ![]() Arriving as part of the game's Summer of Horrors, the update overhauls the night experience. ![]() So I guess the only option for UK gamers right now is to buy the physical edition. 22 hours ago &0183 &32 Here's the terrifying trailer for the upcoming Dying Light 2 update: Good Night, Good Luck. Not too much negative things, only maybe that be the zombie. This is one of the most challenging ports weve seen and Techland has done a remarkable job in scaling down and optimising this brilliant game for a vintage 2015 mobile chipset. It has good gameplay and a good leveling and crafting system. We’ve been told that Techland is working on this availability issue – so be sure to check out the Switch’s store page for confirmation. Dying Light is out soon for Nintendo Switch - and Digital Foundry has exclusive access to the game. This is because the game’s banned in Germany and because the Switch’s digital storefront is ‘technically’ located in Germany – no one in the UK or anywhere else in Europe can download it. Here’s the kicker though – if you want to download the game, you might run into some issues. What is it about these Polish developers that allow them to get these mammoth titles onto the Switch? This is one of the most challenging ports weve seen and. 4. This looks easily as impressive as the Switch port of The Witcher 3. Dying Light is out soon for Nintendo Switch - and Digital Foundry has exclusive access to the game. Maybe this is your first time with Dying Light, or maybe you’re a die-hard fan counting down the days until Dying Light 2? Either way, Dying Light Platinum Edition looks like a phenomenal achievement and should contain hundreds of hours of gameplay. Dying Light Platinum Edition Switch review. Dying Light: Bozak Horde - a challenging game mode with its own side story. Dying Light: The Following - a huge expansion complete with a new story, vast original map, and a customizable buggy to drive. Some new features implemented include touchscreen controls, HD Rumble, motion controls and gyro controls. Generally favorable reviews based on 59 Ratings Your Score 0 Summary: Features: Dying Light - the full award-winning game. As well as the huge amount of content there’s also been improvements to take advantage of The Switch’s hardware. It should be clear by now that this isn’t some ‘lazy port’. So it’s not surprising to see the Switch edition getting loads of love too. The amount of support Dying Light has received over the last 6 years is astounding. It includes the huge ‘The Following’ expansion, a new mode called Hellraid, additional quarantine zones to parkour around as well as a host of other bits and bobs such as weapons and skins. How Techland managed to squeeze this massive game onto Nintendo’s console, I’m not too sure.ĭying Light Platinum Edition is chock full of extra content on top of the 2015 base game. Dying Light, the acclaimed first-person, open-world zombie survival game, is somehow a new Nintendo Switch release. ![]() ![]() ![]() From " Is there gravity on the moon?" to " What is the biggest known star in the universe?" to " Where do pandas live?", we're striving to find answers to the most common questions you ask every day. USA TODAY is exploring the questions you and others ask every day. Just Curious for more? We've got you covered Other examples of renewable energy include wind energy, geothermal energy, hydropower, ocean energy and bioenergy, according to the United Nations. ![]() Solar power can also be converted into thermal or electrical energy. In fact, it is " the cleanest and most abundant renewable energy source available," according to the Solar Energy Industries Association. How hot is the sun? Get to know the blistering temperatures of the star's surface, core Is solar energy renewable? The amount of electricity generated is dependent on how many cells are in each panel: The more PV cells, the more electricity. The electricity is then collected through the negative and positive sides of the cell and flows out. When sunlight hits the PV cell, it releases electrons from the semiconductors. A group of solar panels is called a "solar array." Each cell is made of semiconductor material containing negative and positive receptors, similar to a battery. Solar panels are made of several PV cells, and each produces about one to two watts of power, according to the Office of Energy Efficiency and Renewable Energy. When sunlight radiates to the Earth and onto a solar panel, the energy is absorbed. Photons are found in sunlight, which is a form of electromagnetic radiation. The amount of sunlight that reaches the Earth's surface every hour and 30 minutes is enough to power our planet for a year, according to the Office of Energy Efficiency and Renewable Energy. Solar panels, also known as PV panels, convert sunlight into electrical energy. Solar energy is responsible for sustaining many things, including weather, wind and plant and animal life. This heat, light and energy are all forms of electromagnetic radiation, according to National Geographic. The solar energy that is created is released in the form of waves and particles, which move from the sun throughout the solar system. As these molecules merge, energy is released from the leftover mass. ![]() ![]() This collision has great enough force to form a new element: helium. In the sun's core, hydrogen molecules will collide due to the immense pressure and density. Nuclear fusion is a reaction that occurs in the sun and other stars and creates energy. It is created through a process called nuclear fusion. Solar energy is energy that comes from the sun. Through different technologies, such as solar panels, solar energy can be converted to generate power.īut how do solar panels work? Here is what you need to about solar energy and photovoltaic, or PV, technology. Thanks to the Sun, life on Earth continues. One of the major sources for energy on Earth is the Sun. Each has its own properties and fuel processes that make aspects of life possible, including driving a car or burning a fire. From kinetic and potential to chemical and sound, various forms of energy exist on our planet. ![]() ![]() I swapped all lazy scaled-up portraits with lazy splices. New update, a little later than when I promised to, but it was for a good reason.Ĭhangelog from previous version to this one: Lastly, thanks for playing and Fe4 is my favorite game in the series as well, I plan on doing it justice, so people who are scared of the source’s giant maps can enjoy the story. Oifey is Jegan archetype lol, be he has good growths that’ll allow him to continue being usable until the end of the game, not as good as Leif, Lester or Seliph, but he’ll still be a great unit. And have spawn two Lance Cavaliers on turn 4 as well to add more bit of danger sense. Prologue has been revamped as this: make Harold start moving on turn 4, so you’ll need to run, instead of just waiting. As of chapter 2 units start droping generic iron weapons and by chapter 3 there’s a shop to buy them. And I don’t plan on removing the Rezire tome or nerf it though. I don’t plan on ever having Julia use staffs, she’s already broken with the Rezire Tome and being able to level up just by curing someone will break her even more. I’ll have Lester being fixed in next patch, everyone is saying he is pretty bad(even though he was supposed to be bad since he’s bad iin the source game as well, but I plan on making him usefull) Good luck out there, FE4’s my favourite game in the series. I still enjoyed myself playing this demo, though. But hey, being invincible is kind of his job. In general, the enemies aren’t particularly strong, with only the fear of getting mobbed by a huge swarm of zanbatos proving even vaguely threatening against Oifaye. I’d say add some reinforcements towards the end of the map so you have something to do instead of twiddling thumbs for two turns. The prologue was a bit too simple three sword users easily mopped the floor with Harold’s fighter crew, with two turns to spare defending. Nothing broke on me, but it’s still a concern for me. The lack of equipment is also a bit of a concern when all your units have things like killing edges, not being able to fall down to an iron sword can be troubling. Was Julia’s loss of staff rank intentional? Or did Lana just forget to bring that spare mend with her? For that matter, why is he so bad in general? He can barely damage most enemies, and if he’s given the steel bow, he can’t double anything. However, I have a couple of issues with it as it is right now.įor starters, why doesn’t Lester have Canto? Both Oifaye and Delmud have it, so I presume it’s not a case of removing the skill entirely. I gave the demo a spin last night, and it seems alright. Rossendale, StanH, Leonarth, Teraspark for skills If you feel you should be credited as well,įire Emblem Builder by 7743(I used it to format songs) Me(Yang Kai) for a lot of other songs as well.Ĭircles, Craz圜olorz, Tequila, Teraspark. I know I made: Seliph’s, Leif’s and Julia’s.Ĭredits to whomever made the tohers here: Ishtar is complex mug, it was made by all of the talented spriters:ī.vividria.blackmage Leif(Roy remade) by Phoenix Wright Ragefest, by Blaze Not exactly the same plot/mechanics as the original. I hope you can enjoy it as well, even though it’s I hope you can enjoy this hack of mine and if possibleĪnd for those who played the source game: Hanibal joins too lateĪnd giving Darsim/Xavier to the player would also make them I try to make this hack as close as possible from what’sĪnd yeah, Arden is there, he’s a joke, but the reason he’s So, yeah, this is my version into Fe4’s story.īut don’t worry, I’m not some edgy teenager While I call it remake, all ROMHacking is actually So, what I mean is that, please don’t tell me: ![]() I also plan to make Ishtar and Julius characters to be Some other examples include myself taking some eventsįrom the Manga version and altering it myself. Thracia 776’s characters, like Eyvel, Orsin, Olwen. I’m also adding in some extra stuff, that I feel to I’m setting it to be as close to the source as possible, So, what I mean is that I’m remaking it, and while Then it would be better to go and play the original. It won’t be exactly like the source game was,īecause if it were to be a perfect copy of the source, ![]() So, long-short story, this is my remake idea forįire Emblem 4 - Genealogy of the Holy War. ![]() ![]() ![]() It’s not like playing the game requires the magic of emulating like most Xbox 360-era games, as the game is currently available on PC. Thanks to its perfect balance between over-the-top fun and engaging narrative, the second game is often regarded as the series’ highest point. ![]() Saints Row 2 is one of the most beloved instalments in the franchise. Remake Saints Row 2 Source: Gaming Dragons. Is the game a lost cause? Are the planned DLC contents for the game nowhere near enough to save it? Only time will tell, and although many have dismissed the game and its future endeavors, there might still be hope if Volition make amends with its fanbase instead of further alienating it.Īnd how might they achieve just that? There are two possible solutions to this problem. Unsurprisingly, the reveal was met with dim enthusiasm from the fanbase, a reality tempered with the widespread suspicion that the YouTube Short announcing the roadmap was narrated with an AI voice. The roadmap revealed plans to expand the game in May, July, and August with the release of campaign DLCs, solo game modes, new open-world districts, and quality-of-life improvements. The disappointing display certainly did not seem to discourage Volition from pushing forward as the studio revealed a roadmap for the game’s post-launch content on 27 March. The fact that the game launched at a buggy, unoptimized state certainly didn’t do it any favors, either. Saints Row received significant backlash from the community for its polarizing direction and a ‘betrayal’ towards the game’s more gritty and believable roots. That’s looking at it from a business standpoint community reception to the game has been far less positive. Following the lukewarm reception, Volition’s publisher was transferred from Deep Silver to Gearbox Entertainment, another consequence of the game’s unsatisfactory performance. Although not an outright flop, Volition’s parent company Embracer Group did not see the game as a great return on investment according to a September 2022 article. Launched on 23 August following a delay from a February release window, fans and critics alike were quick to point out the open-world title’s shortcomings, including its technical issues, uninspired gameplay loop, less-than-likable cast of characters, and dull story.Īs such, it should come as no surprise that the game underperformed both financially and critically. The reboot in question, titled Saints Row, can be regarded as one of the most underwhelming game releases of last year. With many decrying the series as ‘dead’ after a disastrous release, the studio presumably wants to make its next step count. You can get the game on GoG before the promo ends here!Īnd also,the link to the community mod is down below.ĮDIT: The game is also free on Steam! You can get the game here.Following an attempted reboot on the crime open-world series Saints Row last year, developer Volition is finding itself at a crossroads. But never fear, as community mod, Gentlemen of The Row, has fix most of the issues the port has. One important thing to note is that the PC port is quite subpar, which even the developers Volition admitted during one of their livestream. Although it is a sequel to the original Saints Row (which is an exclusive title for the Xbox 360), players coming in for the first time won’t need a refresher as it deviates from that title. Set years after the original, the player finds him/herself in a Stilwater both familiar and strange and challenged with bringing the Saints back as the rightful kings of Stilwater and bringing vengeance to those who wronged them. Ever wondered how The Saints initially rise to the top on the streets of Stilwater before the events of Saints Row The 3rd? Well look no further than Saints Row 2, one of the highlight of the series (well, besides IV), now free on GOG for a limited time. ![]() ![]() Natural rubber is one of the best raw materials from which our glue is made. Natural rubber tapes were created with exceptional needs in mind. They are characterized by average resistance to moisture. They are suitable for securing packages of medium and heavy weight. ![]() Hot-melt synthetic rubber belts are replacing natural rubber. By using acrylic tapes, you can confidently protect products intended for transport or storage in the basement. Acrylic tapes are resistant to moisture and naturally appearing aging processes. Acrylic glue has high adhesion, but in difficult conditions its rubber counterparts work better. According to the rule, “what is good for Kowalski does not have to suit Nowak”, we made wrapping tapes on a different adhesive basis.Īcrylic tapes, due to the fact that they belong to “thermophilic” materials, are perfect at positive temperatures, in packing not too heavy goods, they will prove themselves in office work. The self-adhesive tapes we have created have not been produced in bulk with everyone in mind, but to meet the unique needs of our customers. Self-adhesive tapes for the unique needs of our customers We also offer a silent tape – more and more often used self-adhesive tape, ensuring comfort and silence during packing, and does not emit a characteristic sound when unwinding.ĭue to the wide range of products, even the most demanding package will be perfectly protected thanks to us. Solvent (natural rubber) – a self-adhesive tape with a very aggressive adhesive strength, with an adhesive layer based on solvent adhesive (natural rubber) with natural resins, with resistance to low temperatures, for industrial and general use, for sealing the most demanding cartons, both by hand and automatic.Īll kinds of hand tapes can be transparent or brown, they can also be machine-wound. Suitable for packing large, medium and light cardboard boxes. Such an adhesive tape is resistant to moisture and has a high adhesive strength. Hot-melt (synthetic rubber) – thanks to its advantages such as stickiness, flexibility, as well as the gloss of the carrier and transparency, typical of polypropylene tapes, is widely used in the packaging sector. Suitable for packing medium and light cardboard boxes. The stickiness of the tapes and the flexibility of the carrier, typical of polypropylene tapes, make the product more and more often chosen as an alternative to rubber tapes. ![]() Thanks to it, the tapes are resistant to temperature changes and moisture, while maintaining their properties.Īcrylic – it is eco-friendly, so the acrylic adhesive tape is completely environmentally friendly in the production process as well as in use. ![]() Such tapes are stretchy, connect well, and thanks to the “varnish” coating used – glossy. Packaging tapes should be adapted to different packages, depending on their weight with the product. Correct selection of the width, strength of the glue and the type of material the adhesive tape was made of will provide an effective protective barrier for each package. They are mainly used to secure various packages and protect their contents. Which, with appropriate adjustment to the requirements, will ensure that our self-adhesive tape will properly secure each shipment.Īdhesive tapes were probably used by everyone. The adhesive tapes we offer may be on one of the three types of glue: ![]() ![]() I mean, the places where we differed on COVID. His family has treated the presidency like a business opportunity. He mocks evangelicals behind closed doors. The way he treats women, and spends like a drunken sailor, the ways I criticized President Obama for that kind of spending, I criticize President Trump for it as well. It isn’t just that he fails to lead our allies, is that the United States now regularly sells out our allies under his leadership. I mean, he and I have a very different foreign policy. He hasn’t lifted a finger on behalf of the Hong Kongers. I mean, the way he ignores that the Uighurs are in literal concentration camps in Xinjiang right now. And I’m not at all apologetic for having fought for my values against his in places where I think his are deficient, not just for a Republican, but for an American. ![]() And these aren’t just mere policy issues. But, as your question says, there are obviously a lot of places where he and I differ as well. So there are definitely places where we agree. I’m 48 years old and I’m the first Nebraskan on the committee since the mid 70s. I’m the first Nebraskan on the judiciary committee in I think 46 years. In fact, I went on the judiciary committee after he was elected, explicitly to advocate for the kind of originalist and constitutionalist that he had put on his list, and that he had agreed to nominate. So, for example, one of the places where he’s changed, as we were just mentioned to the last questioner, is I think he’s nominated truly great judges, and I worked with him on that. ![]() Or maybe a better way to put it is, where the president has now adopted traditionally Republican positions that he used to reject for the majority of his life when he was funding Democratic candidates. But Donald Trump is our president now, so I’ve worked hard to develop a good relationship with him, he’s got a hard job, and we’re called to pray for our leaders, so that’s what we do regularly at the breakfast table at our house, is we pray for the president, and the First Lady, and for Vice President Pence in their callings.Īnd there are obviously a number of issue areas where president trump and I have policy alignment now. I obviously campaigned for a lot of other people in the 2016 cycle. So I’ve worked hard to develop a good working relationship with the president over the last three and a half years. I think we should distinguish between policy agreement and policy disagreement, and then also, long term political implications as well. And I guess, I kind of think about it like this. Why do you have to criticize him so much? I think, like a lot of Nebraskans, I’m trying to understand your relationship with the president. ![]() ![]() ![]() Windows, by default, has no idea what a TAR.GZ file could possibly be. For example, see ist from macOS Mojave 10.14.5 for details. To open or extract a tar.gz file on Windows, you can install the free 7-Zip File Manager utility, or you can use the tar -xvf command from the Bash prompt included in the Windows Subsystem for Linux. The most common tool for this task is xz-utils. unp Here is a little summary from its man-page: unp is a small script with only one goal: Extract as many archives as possible, of any kind and from any path to the current directory, pre serving the subdirectory structure where needed. ![]() Unless you care about the technical details. To unzip XZ files in Linux, we need a tool that can handle the LZMA/LZMA2 compression. This is the only feasible solution looking forward with more and more archive types coming. Drag and drop a TAR.XZ file or click Browse device to select a file to extract. (2.8.3 is still used in Mojave, albeit with various, minor-looking, darwin-specific patches accumulated over the years if I understand correctly. Some text editing programs can open XZ files and display the contents without unzipping them. at 19:27 Better Question to ask than how to do this with tar: Use unar or 7z and never worry about choosing the right program for your type of archive again. How to extract TAR.XZ files online Select file. And OS X 10.7.x shipped with libarchive 2.8.3. OS X 10.6.x shipped with libarchive 2.6.2. The feature is present back to macOS 10.7, but it is configured off until macOS 10.9.įound some info about OS X and libarchive versions. For example, OS X Mountain Lion does not have /usr/lib/liblzma.dylib, nor /usr/lib/liblzma.5.dylib, see this post and the table from this post.Īs this StackOverflow answer rightly points out, the xz/lzma feature of bsdtar is configurable at compile time. xz can not be extracted by the native gunzip on OS X because this library is not present. Note: The library liblzma is required to extract. xz files - so it is sure to also work on Yosemite. In Mavericks (10.9.5), you can use gunzip in a terminal to extract. UnZiper is an incredibly helpful and easy-to-use online tool that makes it possible to extract, compress, or convert compressed files in an instant. ![]() ![]() Satisfaction Guaranteed: You may use TurboTax Online without charge up to the point you decide to print or electronically file your tax return.If we are not able to connect you to one of our tax professionals, we will refund the applicable TurboTax Live Business or TurboTax Live Full Service Business federal and/or state purchase price paid. We will not represent you before the IRS or state tax authority or provide legal advice. If you receive an audit letter from the IRS or State Department of Revenue on your 2022 TurboTax business return, we will provide one-on-one question-and-answer support with a tax professional, if requested through our Audit Support Center, for audited business returns filed with TurboTax for the current 2022 tax year. TurboTax Audit Support Guarantee – Business Returns.You are responsible for paying any additional tax liability you may owe. If you pay an IRS or state penalty or interest because of a TurboTax calculation error, we'll pay you the penalty and interest. 100% Accurate Calculations Guarantee – Business Returns.(TurboTax Free Edition customers are entitled to payment of $30.) This guarantee is good for the lifetime of your personal, individual tax return, which Intuit defines as seven years from the date you filed it with TurboTax. If we are not able to connect you to one of our tax professionals, we will refund the applicable TurboTax federal and/or state purchase price paid. Audit Support Guarantee – Individual Returns: If you receive an audit letter from the IRS or State Department of Revenue based on your 2022 TurboTax individual tax return, we will provide one-on-one question-and-answer support with a tax professional, if requested through our Audit Support Center, for audited individual returns filed with TurboTax for the current 2022 tax year and, for individual, non-business returns, for the past two tax years (2021, 2020). ![]() (TurboTax Online Free Edition customers are entitled to payment of $30.) This guarantee is good for the lifetime of your personal, individual tax return, which Intuit defines as seven years from the date you filed it with TurboTax. Maximum Refund Guarantee / Maximum Tax Savings Guarantee - or Your Money Back – Individual Returns: If you get a larger refund or smaller tax due from another tax preparation method by filing an amended return, we'll refund the applicable TurboTax federal and/or state purchase price paid.This guarantee is good for the lifetime of your personal, individual tax return, which Intuit defines as seven years from the date you filed it with TurboTax. 100% Accurate Calculations Guarantee – Individual Returns: If you pay an IRS or state penalty or interest because of a TurboTax calculation error, we'll pay you the penalty and interest. ![]() ![]() ![]() License: CC BY-SA: Attribution-ShareAlike Free High School Science Texts Project, Sequences and series: Arithmetic & Geometric Sequences, Recursive Formulae (Grade 12).Kenny Felder, Advanced Algebra II: Conceptual Explanations.License: Public Domain: No Known CopyrightĬC licensed content, Specific attribution This right over here is a recursive definition. Term, a sub k, is going to be the previous Starting at k, theįirst term, a sub 1, is going to be 3, now. So how would we do this one? Well, once again, we could And I'm just going to add 3įor every successive term. Sequence, when I said, hey, I'm just going to start with 1. ![]() What we mentally did when I first wrote out the Well, what about a sub 3? Well, it's going to beĪ sub 2 plus 3. What happens when k equals 2? Well, they're saying, well, it's Now, how does this make sense? Well, we're defining The previous term, plus- in this case, we'reĪdding 3 every time. And so then weĬould write a sub k is equal to the previous term. Sequence recursively, you want to define what yourįirst term is, with a sub 1 equaling 1. We could say a sub k, starting at k equalsġ and going to 4 with. So how would we do that? Well, we could also-Īnother way of defining this first sequence, And I want to be clear- notĮvery sequence can be defined as either an explicitįunction like this, or as a recursive function. It, especially something like an arithmetic sequence, weĬan also define it recursively. These functions? Well, we can also define Say, well, what's another way of defining Now, in both of theseĬases, I defined it as an explicit function. Term and goes to infinity, with a sub k is equaling. This sequence as a sub k, where k starts at the first Wanted to define it explicitly as a function- we could write This is a sub 2- all the way to infinity. And here, we're goingįrom our first term- so this is a sub 1, But I could use the notationī sub k or anything else. This is equal to- and people tend to use a. Now, how would I denote thisīusiness right over here? Well, I could say that The domain, is restricted to positive integers. Traditional function notation, I could have written I have essentially defined a function here. So this is one way to explicitlyĭefine our sequence with kind of this function notation. Times 3, or maybe I should write 3 times k Here, I could say a sub k is equal to some function of k. Sequence, I could define it as a sub k from k equals 1 toĤ, with- instead of explicitly writing the numbers It defining our sequence as explicitly using kind of aįunction notation or something close to function notation. Now, I could also define itīy not explicitly writing the sequence like this. So this just says, all of theĪ sub k's from k equals 1, from our first term, all This right over here is the sequence a sub kįor k is going from 1 to 4, is equal to thisĪt it this way, we can look at each of these as But I want to make usĬomfortable with how we can denote sequences andĪlso how we can define them. Of different notations that seem fancy forĭenoting sequences. So we could call thisĪn infinite sequence. Pattern going on and on and on, I'll put three dots. This is infinite, to show that we keep this Keep adding the same amount, we call these Infinite sequence- let's say we start atģ, and we keep adding 4. So this one we wouldĬall a finite sequence. And let's say I only have theseįour terms right over here. Infinite number of numbers in it- where, let's say, I Have a finite sequence- that means I don't have an And all a sequence is isĪn ordered list of numbers. Video is familiarize ourselves with the notion of a sequence. I assume for quizzes however that they will continue to specify the start 1, so just work around it. You can easily avoid this problem in your own work by explicitly starting your K to start at 0. In modern Computer Science(Programming), we don't work with Indexes like this any longer, and starting an Index at 1 is generally fallen out of fashion largely in part of this constant need to work around the problem. We need to subtract 1 to bring back that balance. The current Index can be seen as offset by 1 due to starting at 1. If We look at K=1 and did not subtract 1 from the current index we would actually get 1+3(1) = 4 or 1+3(2)=7. This number increments each time across the "loop" and can be seen as similar to the Sigma∑ notation's looping functionality in that respect.) PreNote: ( k=1 is an index location, like finding a book in a library. This is essentially a "hack" to avoid counting your current "index" location against the math. ![]() |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |