# Series convergence

• January 15th 2013, 12:32 PM
Lisa91
Series convergence
I have two series:
$\sum_{n=13}^{\infty} (-1)^{\left\lfloor \frac{n}{13} \right\rfloor} \frac{lnn}{nln(lnn)}$. I wanted to 'group' terms but I had a problem with idices.

$\sum_{n=1}^{\infty} (-1)^{n} \frac{2lnn}{(n+1)^{0,5}}$ I tried the Leibniz's, Dirichlet's, Abel's tests but they gave me nothing. Any hints how to cope with them? :(
• January 15th 2013, 01:16 PM
ILikeSerena
Re: Series convergence
Hi Lisa91! :)

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 $\lim_{n \to \infty} {2 \ln n \over (n+1)^{0.5}}$?
• January 15th 2013, 01:24 PM
Lisa91
Re: 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.
• January 15th 2013, 01:30 PM
ILikeSerena
Re: Series convergence
Yes, it is zero.
So if it is also decreasing, we can apply Leibniz.