- #1

- 1

- 0

## Homework Statement

The coefficients of the power series the sum from n=0 to infinity of an (x-2)^n satisfy ao=5 and an= [(2n+1)/(3n-1)] an-1 for all n is greater than or equal to 1. The radius of convergence of the series is

A) 0 B) 2/3 C) 3/2 D) 2 E) infinite

## Homework Equations

## The Attempt at a Solution

Convergence test: lim n→∞|an (x-2)^n / an+1 (x-2)^n+1|

2/3*|1/(x-2)|<1

x belongs to (4/3, 8/3)

Therefore, the radius is 2/3