calculus - Determine the convergence of the following series $sum_{n=2}^{infty} (-1)^n frac{1}{sqrt{n} + (-1)^n}$

$\sum_{n=2}^{\infty} (-1)^n \frac{1}{\sqrt{n} + (-1)^n}$

Now i know that this is alternating series which means that i should determine the absolute convergence $|a_n|=\frac{1}{\sqrt{n} + (-1)^n}$ but i don't know how to do it, d'Alembert's test isn't working Cauchy tests can't help here here either so i am out of ideas now.