Q. 61 - Calculus

Question

Let $\sum _{k=0}^{\mathrm{\infty }} a_k{x}^k$ be a power series in $x$ with a finite radius of convergence $p$. Prove that if the series converges absolutely at either $\pm p$, then the series converges absolutely at the other value as well.

Step-by-Step Solution

Answer

Ans: 

Step 1. Given information.

given,

      $\sum _{k=0}^{\mathrm{\infty }} a_k{x}^k$

Step 2.