$\sum 0$: does it converge or diverge?

Question

Sometimes I have to do exercise with parameter and, if I substitue particular value of the parameter, I obtain $\sum_{n=1}^{\infty} 0$. But it isn't clear for me if in this case the series converges or diverges.

Answer 1

This series converges to zero. Let $s_k = \sum_{n=1}^{k}0 = 0$, then $$ \sum_{n=1}^{\infty}0 = \lim_{k\rightarrow\infty} s_k = \lim_{k\rightarrow\infty} 0 = 0. $$