Question

Give precise mathematical definitions or descriptions of the concept that follows. Then illustrate the definition or description with a graph or an algebraic example.

radius of convergence

Short answer

A power series' radius of convergence is the radius of the biggest disc at the series' center where the series converges.

Step-by-step solution

Step 1. Given information

Concept is "Radius of convergence"

Step 2. Explanation

A power series' radius of convergence is the radius of the biggest disc at the series' center where the series converges. It is either a non-negative real number or the $\infty$.

For example: Radius of convergence of the power series$\sum _{n=1}^{\infty }\frac{{\left(-1\right)}^n{\left(x-5\right)}^2}{\sqrt{n}}$is 1.