This is a very simple question, but I just wanted to to make sure. The question asks to find whether or not the series [k(k+2)]/[(k+3)^3], k=1 to infinity, converges or diverges, and if it converges, to find the sum. So I used the limit method and found that the limit as k goes to inifinity is 1. The book says that the limit has to go to 0 for it to converge, so does this mean that the series diverges since the limit is 1 (if that is in fact the answer)?