Need help on this series test for convergence or divergence

rodneyram

1. The problem statement, all variables and given/known data

The equation is the summation from n=1 to infinity of [(-1)^n] / [sqrt(2n+3)].

2. Relevant equations

If the series An is compared to a a series Bn that diverges and the series An is greater than the series Bn they both diverge.

If the limit from n to infinity of An/Bn is greater than 1, they both converge or diverge.

3. The attempt at a solution

Can I compare this to 1/sqrt(2n), which is greater than the main problem, and then use the limit comparison test to conclude that the series diverges?

Is this correct?

micromass

It wouldnt work in this case. The series 1/sqrt(2n) is greater then the main problem, but diverges. This doesn't mean that the smaller series has to diverge. In fact, I think that the series in your problem converges.

Have you heard of one of the following: Abels criterion, Dirichlets criterion, Leibniz criterion?

rodneyram

No, I haven't heard of any of those.

I used the limit comparison test on the two series sqrt(2n)/sqrt(2n+3) which equals to one. Doesn't that prove they are both divergent because the limit is greater than 0 due to the limit comparison test?