This special class of power series plays an important role in mathematics, for instance for the study of ordinary generating functions in combinatorics and the summation of divergent series in analysis.

Dec 3, 2025 · There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p (x_1,...,x_n)=sum_ (k=1)^nx_k^p, (1) and the second is the …

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.

Nov 11, 2025 · In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series.

In this video, we use a Maclaurin Series (Taylor Series centered at 0) for cosine to find the sum of the given series.

Any tips on solving the sum of series/power series? See polylogarithm. You can find the second sum using the first with $x = 1/3$.

Jan 24, 1998 · Most series don't have a closed-form formula, but for those that do, the above general strategy usually helps one to find it.

This calculator will try to find the infinite sum of arithmetic, geometric, power, and binomial series, as well as the partial sum, with steps shown (if possible). It will also check whether the series converges.

Jan 5, 2016 · I know one method is to do substitutions and getting the series into a form of a known series. So far I've converted the series into $$ 1 + \frac {2} {x} + \frac {3} {x^2} + \frac {4} {x^3} + …

Jul 4, 2024 · To find approximate solutions to problems in the sciences, it is often necessary to calculate the sum of a finite or infinite series. There are a variety of formulas that are used to accomplish this. …