Classify as absolute convergent, conditionally convergent or divergent:
$$\sum\limits_{n=1}^{\infty} \frac{(-1)^n (\tan^{-1})n}{(n^2+1)}.$$
Answer is absolute convergent, I justify by using p-series. Can someone tell me if its right or wrong to use p-series? My working is $\sum\limits_{n=1}^{\infty}$ $|\frac{(-1)^n (\tan^{-1})n}{(n^2+1)}|$ = $\sum\limits_{n=1}^{\infty}$ $\frac{(\tan^{-1})n}{n^2+1}$
By p-series, it converges. But how do I show it converges absolutely?