The definition I am working from is "Let Z=(z(sub n)) be a decreasing sequence of strictly positive numbers with lim(Z)=0. Then the alternating series, Sum(((-1)^n)*Z) is convergent. My question is how to solve the following: If the hypothesis that Z is decreasing is dropped, show the Alternating Series Test may fail. I am aware of a proof utilizing some Z that is also alternating, but this breaks the condition that Z is strictly positive. I am unaware of an such sequence that has a limit of 0, all elements of the series are positive, yet is divergent. This question is due within 10 hours. Please help!