Not only are there dozens of calculators organized by subject – algebra 1 and 2, calculus, linear algebra, statistics, and more – you can also access math games, logic puzzles, and answers to previously submitted math questions. This site also offers students many tools and resources to choose from. You can, however, customize and embed the calculator on your own web page or easily share it with others. Unfortunately, you cannot access the steps by which the equation was performed. The convergence calculator is easy enough to use and only requires numbers and text in three fields to produce both the geometric series formula and the sum for a finite series. In addition to its web-based tools, it also has subject-specific and reference mobile apps for the iPhone, iPad, Kindle fire, Android, and Windows. Wolfram|Alpha’s goal is to help people at all skill levels perform dynamic calculations on their own as opposed to hunting endlessly through the Internet for a specific answer. With over sixty million registered users, a free account lets you store up to ten problems as well as do practice problems on a single topic.Ī paid account offers additional features such as no ads, a mobile app, unlimited storage, and thousands of practice quizzes. In addition, you can access absolute convergence and power series calculators. On the convergence calculator page, it’s simple enough to use the available math symbols to create your geometric series formula.Īfter that, you’ll receive not just the answer but also a step-by-step solution with accompanying explanations along the way. Plus, you can use scientific notation and math symbols as opposed to just inputting numbers and text. The Symbolab website provides multiple calculators to perform functions using integrals, equations, limits, tangent lines, and more. Or, if you’re using a TI-83 or TI-84 Plus, you can skip straight to the section to download programs to perform this function on your graphing calculator. Convergence CalculatorsĪs you’ll see below, there are many different online convergence calculators to choose from.Įach one, however, offers slightly different options and levels of accompanying information. See, that’s not complicated at all! Or to put it another way, that’s why there are a variety of convergence calculators available to do the heavy lifting for you. To see an example problem solved, check out this detailed step-by-step solution. Plug in your geometric series values to the S= a1/(1− r) formula to calculate its sum.Find the first term by using the value of n from the geometric series formula.That is, if the value of r is greater than one, the sum of the series is infinite. Identify the value of r from the geometric series formula.There are four steps to determine if an infinite geometric series has a finite sum and, if so, what that sum is: Therefore, the finite sum S of a geometric series where −1 < r < 1 is determined by the formula S= a1/(1− r). If r is greater than 1, however, the sum of the series is infinite and is represented by the ∞ symbol. When the value of r is between −1 and 1, you can calculate the finite sum of an infinite geometric series. The basic form of a geometric series is a1 + a1* r + a1* r^2 + a1 r^3 +… so that a1 is the first term and r is the common ratio. The key distinction here, however, is whether the sums of these infinite series are finite (converging on a certain number such as 1/2) or infinite by only becoming larger into infinity. Calculate the Sum of a Convergent Geometric seriesįirst, there needs to be a distinction made in the way “infinite” is being used.īoth the sample series above are infinite: the first approaches 1/2 without ever reaching it – there will always be more numbers in the series but they will become smaller and smaller – while the second series is infinite as it adds more, larger numbers forever. On the other hand, if you have 10 + 20 + 40 + 80 … the sum of the series only continues to become larger, making it infinite.Īs with most other calculus equations, you can determine if the sum of a series is finite or infinite as well as the sum of a finite series by hand, and it’s not a bad idea to know how to do it this way.įor speed and ease, however, there are several different types of convergence calculators you can use which we’ll go over below. One exception to this, however, is when you’re working with an infinite geometric series, and you need to determine whether its sum is finite or infinite.įor example, if you have 1/4 + 1/8 + 1/16 … the sum of this infinite series will ultimately approach – that is, converge upon – 1/2, and that makes its sum finite. Even in a second-semester calculus class, determining the sum of an infinite series is beyond the scope of what you’ll typically be asked to do.
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