I have a few problems concerning infinite series which I need some help on. I'm supposed to determine the convergence/divergence using ONLY the comparison tests. Here are the problems:
For the first and the third ones, I want to apply the plain comparison test, using as the series which I compare it to. However, I need a way to prove that is greater than for all n [1, . Once I prove this, how would I apply it to the third problem since it's ? By the way, that is e^n^2...it's kind of hard to tell with the latex. For the second problem, here is what I have so far:
So, now using the limit comparison test...
The limit exits, is finite, and is greater than zero...so the original series will behave the same as but I'm not sure how to prove whether this series converges/diverges? Any help would be appreciated.