Basic Analysis I — Real Analysis · Problem 2.6.9

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · power-series-ratio-test

Problem

Figure out how to compute the radius of convergence using the ratio test. That is, suppose

\sum_{n=0}^{\infty} a_n x^n

is a power series and

R := \lim_{n \to \infty} \frac{|a_{n+1}|}{|a_n|}

exists or is

\infty

. Find the radius of convergence and prove your claim.