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 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 …

In mathematics, a power series (in one variable) is an infinite series of the form where represents the coefficient of the n th term and c is a constant called the center of the series.

To explain the difference between Taylor’s theorem and power series in more detail, we introduce an im-portant distinction between smooth and analytic functions: smooth functions have …

This section contains lecture video excerpts, lecture notes, problem solving videos, and a worked example on power series.

Since the terms in a power series involve a variable x, the series may converge for certain values of x and diverge for other values of x. For a power series centered at x = a, the value of the …

Power series are used to approximate functions that are difficult to calculate exactly, such as tan -1 (x) and sin (x), using an infinite series of polynomials.

Any power series can give an approximation about the center of the series, denoted by the constant c c above. A power series will converge provided it does not stray too far from this …

Dec 1, 2025 · The power series ∑ n = 0 ∞ a n x n is an infinite series, and looks like a function of x. An easy way to illustrate the idea of a power series representing a function is to use the …

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 …