It is given that the series $\sum_{n=1}^\infty a_n$ is convergent, but not absolutely and $\sum_{n=1}^\infty a_n=0$. Denote by $S_k$ the partial sum $\sum_{n=1}^k a_n$ , $k=1,2,\dots$ Then,
(a) $S_k=0$ for infinitely many $k$;
(b) $S_k>0$ for infinitely many $k$ , $S_k<0$ for infinitely many $k$;
(c) it is possible that $S_k>0$ for all $k$;
(d) it is possible that $S_k>0$ for all but finite number of values of $k$.
I am completely stuck on it. How can I solve this problem? Please help.