I have two series:

$\displaystyle \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.

$\displaystyle \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?