1. The problem statement, all variables and given/known data I'm given this series and asked whether it converges, absolutely converges, or diverges. Ʃ(n=0 to infinity) [2(-1^n)(3^(n+1))]/5^n 2. Relevant equations 3. The attempt at a solution The answer states that it is absolutely convergent, and that it converges to 15/4. Everything I've done doesn't get me to this answer. It's driving me nuts! On the one hand, we can say it's an alternating series. So, by the alternating series test, I took the limit of b_n, and right off the bat, I can't seem to get that to equal 0, which by the alternating series test, would say that the series diverges. So then, I tried the ratio test. I know that for the ratio test, if the limit of the ratio is < 1, the series converges. If I pull out the 2 and then use the ratio test, I do in fact get a number that is < 1, but multiplying it by 2, doesn't get me anywhere near 15/4. I really don't know where to go from here. Obviously I'm using these tests incorrectly, but I can't see how... :/ Anyone help would be greatly appreciated!