1. ## Quick question

We have $\sum_1^\infty (-1)^ka_k$.

If $\lim_{k->\infty} a_k>1$ does $\sum_1^\infty (-1)^ka_k$ diverge by the Divergence Theorem?

2. Originally Posted by paupsers
We have $\sum_1^\infty (-1)^ka_k$.

If $\lim_{k->\infty} a_k>1$ does $\sum_1^\infty (-1)^ka_k$ diverge by the Divergence Theorem?
Yes. It diverges.

If $\lim_{n\to\infty} |a_k| \neq 0$, then $\lim_
{n\to\infty} (-1)^k a_k$
does not exist.

Thus $\sum_{n \geq 1} (-1)^k a_k$ diverges.