How do I check the series $\sum_{n=2}^{\infty} \frac{(-1)^n }{n+(-1)^n}$ for absolute convergence/conditional convergence?

How do I check the series $\sum_{n=2}^{\infty} \frac{(-1)^n }{n+(-1)^n}$ for absolute convergence/conditional convergence ?

How can I solve this problem?


hint

for $n\geq 2$,

$$|\frac {(-1)^n}{n+(-1)^n}|=\frac {1}{n+(-1)^n} $$

$$\geq \frac {1}{n+1}$$

thus id doesn't converge absolutely.