Convergence question

• Apr 10th 2008, 12:40 PM
lllll
Convergence question
Use the integral test to determine whether the series converges: $\sum^{\infty}_{n=1} \frac{1}{(2n+1)^3}$

I was thinking instead of using the integral test I just make $(2n+1) = x$ which becomes $\sum^{\infty}_{n=1} \frac{1}{(x)^3}$ which is a p-series and is clearly convergent. Would that be a valid assumption?
• Apr 10th 2008, 12:43 PM
ThePerfectHacker
Quote:

Originally Posted by lllll
Use the integral test to determine whether the series converges: $\sum^{\infty}_{n=1} \frac{1}{(2n+1)^3}$

I was thinking instead of using the integral test I just make $(2n+1) = x$ which becomes $\sum^{\infty}_{n=1} \frac{1}{(x)^3}$ which is a p-series and is clearly convergent. Would that be a valid assumption?

Do not use integral test, $0 \leq \frac{1}{(2n+1)^3} \leq \frac{1}{n^3}$.