# Thread: testing series for convergence or divergence

1. ## testing series for convergence or divergence

$\sum_{k=1}^{\infty} \frac{(-3)^{k+1}}{4^{2k}}$

$\sum_{m=1}^{\infty} (\sqrt[m]{3}-1)^m$

Help!

2. ## Re: testing series for convergence or divergence

I think the comparison test is used for the first one

3. ## Re: testing series for convergence or divergence

Originally Posted by tinspire
I think the comparison test is used for the first one
with a bit of algebra the series in (a) can be put in the form of a geometric series

4. ## Re: testing series for convergence or divergence

I suppose the 2nd one requires root test: Pauls Online Notes : Calculus II - Root Test

As m approaches infinity, the limit of the mth root of the sequence will approach 0. Since it's less than 1, the series converges. Correct me if I'm wrong though.

5. ## Re: testing series for convergence or divergence

so is the first one comparison? or is that one also by root test?