Thread: Does this alternating series necessarily converge?

If a0, a1, a2,... is a nonincreasing sequence of positive numbers that converges to 0, does the alternating series SUMMATION [(-1)^k]ak necessarily converge?

I'm having trouble grasping the concept here, any insight is greatly appreciated.

If the terms are non-increasing and converge to zero and you have alternation then it does converge.