1. The problem statement, all variables and given/known data The problem contained five answer choices, of which I the answerer was to find one that fit the criteria of the question. The question was: "Which series of the following terms would be convergent?". It listed five series, The answer was this term: 1 + (-1)n / n. 2. Relevant equations [itex]\Sigma[/itex]1 + (-1)n / n. 3. The attempt at a solution I find this very confusing simply because whilst separating the series into two separate series, [itex]\Sigma[/itex]1 and [itex]\Sigma[/itex](-1)n / n, The second series converges (yes I was surprised also) by the alternating series test. Originally, I was dumbfounded because of the absolute value test, so I suppose the series is conditionally convergent. Anyways, if [itex]\Sigma[/itex](-1)n / n is convergent and [itex]\Sigma[/itex]1 is divergent, 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1.... + 1 .... +1 (you get the point) Then how can a finite number (the second alternating series) affect convergence? Also, the limit test kind of rules convergence out for this one. Ha. I may be missing something deceptively simple, so if anyone can help me out here that'd be great!