1. The problem statement, all variables and given/known data There are three problems that I am struggling with. 1. ∑[k2(x-2)k]/[3k] 2. ∑[(x-4)n]/[(n)(-9)n] 3. ∑[2k(x-3)k]/[k(k+1)] 3. The attempt at a solution On the first two I am having problems finding the end-points of the interval of convergence. I use the ratio test. 1. ∑[k2(x-2)k]/[3k] Here I get I = (1,3) 2. ∑[(x-4)n]/[(n)(-9)n] I = (-13,5) And in the last one I got the end-points but I am not sure why the left one would diverge. It says it diverges in the answers but I cannot see it. 3. ∑[2k(x-3)k]/[k(k+1)] I = [5/2,7/2) I use the alternating series test to evaluate x=5/2 and it doesn't seem to go to zero. I do l'hopitals, but it always shows me that it diverges.