# Thread: f' and f'' interval of convergence

1. ## f' and f'' interval of convergence

Given f(x) = (x^n)/(n)^2, find the interval of convergence of f' and f''.

What I got: after doing the ratio test for the original series, I found out that R = 1 and the interval of convergence is [-1, 1]. And I know that for f' and f'', the R value is the same and the interval of convergence is also the same, except that we've to check the endpoints. But what I don't get is how do I find the IOC for f' and f''. Do I have to use the ratio test again?

2. Originally Posted by Taurus3
Given f(x) = (x^n)/(n)^2, find the interval of convergence of f' and f''.
[snip]
Is there meant to be a summation sign somewhere?

3. oh sorry! Yes, as n goes from 1 to infinity.