Q 4. - Calculus

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

Step-by-Step Solution

Answer

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

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.