I have two series:

. I wanted to 'group' terms but I had a problem with idices.

I tried the Leibniz's, Dirichlet's, Abel's tests but they gave me nothing. Any hints how to cope with them? :(

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- Jan 15th 2013, 12:32 PMLisa91Series convergence
I have two series:

. I wanted to 'group' terms but I had a problem with idices.

I tried the Leibniz's, Dirichlet's, Abel's tests but they gave me nothing. Any hints how to cope with them? :( - Jan 15th 2013, 01:16 PMILikeSerenaRe: Series convergence
Hi Lisa91! :)

Let's start with the second.

You said you tried Leibniz and that it gave you nothing.

From the formula there's a pretty good match with Leibniz's test, so let's investigate.

Can you find ? - Jan 15th 2013, 01:24 PMLisa91Re: Series convergence
Well, I suppose it's 0 but I'm not so sure I know how to prove it. I wanted to show that the sequence declines but I couldn't finish it.

- Jan 15th 2013, 01:30 PMILikeSerenaRe: Series convergence
Yes, it is zero.

So if it is also decreasing, we can apply Leibniz.

Let's start with the first criterion.

Are you aware of l'Hôpital's rule? - Jan 15th 2013, 01:30 PMSworDRe: Series convergence
The "power" of any log is 0, and the power of the denominator is 0.5, so the ratio will go to 0.

- Jan 16th 2013, 02:05 PMILikeSerenaRe: Series convergence
I'm guessing that's a no?