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.

a series is absolutely convergent if $\sum |a_n| < M$
If a series is absolutely convergent then every sub-series is convergent.
Consider  $\sum (-1)^n|a_n|$
The sum of the of the even terms converges, the sum of the odd terms converges.
