real analysis - If a sequence of absolute values is bounded, does it then converge?

I'm stuck on an easy proof. I have a bounded sequence $\sum\limits_{k=1}^{n}|x_{k}|$ and I need to prove that it converges. I don't see how this would work. I don't see how I could use cauchy and also I don't see why this sequence would have to have a limit.

EDIT: thanks to the tips the solution was easy. Another proof for the convergence of the sequence $\sum\limits_{k=1}^{n}x_{k}$ must be given. Now I cannot use monotonically increasing sequence. I was thinking about rearranging $S_{n}$ in a way that it becomes monotonically increasing but I don't know if that is allowed. Any suggestions?

Answer

Hint: The sequence is monotonically increasing.