Nov 16, 2022 · To use the Geometric Series formula, the function must be able to be put into a specific form, which is often impossible. However, use of this formula does quickly illustrate how functions …

In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power series.

In this video, I break down the process into 3 main cases, and work through lots ...

There are many functions which can be represented by power series, and how to generate them will be covered in the next concept. Listed below are some common functions, their power series forms, and …

We take that series, and replace $r$ with $x$, getting a power series. We can express this as a function, as you see below below, as long as $|x|<1$. The video will look at these and other examples arising …

In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power series. Calculus …

Jun 6, 2025 · Power series are central to many concepts in calculus. They help express complicated functions as sums of simpler terms. This is useful because, near a specific point, a power series can …

Creating Power Series Representations for Other Functions. By manipulating the expressions in equation (3), we can represent other functions as powers series. This manipulation includes algebra, …

Jul 23, 2025 · When we talk about a converging power series, we mean that as you add more terms, the series approaches a finite value. The key concepts here are the radius of convergence and the …

We can modify f(x) to get power series for related functions. For example, if we substitute 1 x into the series for f(x), we get a power series with center x = 1: