Convergence question

**lllll** · April 10th 2008, 11:40 AM

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?

**ThePerfectHacker** · April 10th 2008, 11:43 AM

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, $0 \leq \frac{1}{(2n+1)^3} \leq \frac{1}{n^3}$ .

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