Can an alternating series ever be absolutely convergent? Can an alternating series EVER be absolutely convergent?
I am examining practice problems in my calculus book and I haven't yet come across a case where this is so.  It might be because they are simple, but I'm genuinely curious.

Hint: You could take any (absolutely) convergent series $\sum_{n=0}^\infty{a_n}$ where $a_n> 0$, and then consider $\sum_{n=0}^\infty{(-1)^na_n}$.
