series of functions - find the value of x for which the series converges

series of functions - find the value of x for which the series converges

Can you help me to find out, what is the value of x (real) so the
following series converges?
the series is: (n->infinity)
(-1)^n * (log(n+x^2)) * (1/(n^(1/4))
I hope it's clear, I tried to use Leibnitz, Abel and Dirichlet but I just
don't succeed and I'm frustrated.