So, I actually have a bunch of these problems and I cannot do any of them. I don't think I'm really understanding it. Here is the question: (one of them) The way I wrote them, a_n means a sub n
For each sequence a_n find a number k such that n^k a_n
has a finite non-zero limit.
(This is of use, because by the limit comparison test the series ∑from 1 to infinity (a_n) and ∑from 1 to infinity (n^-k) both converge or both diverge.)
What does k equal?
The Attempt at a Solution
I'm actually 100% lost on this problem. I don't even know where to start :(
Here's my attempt. It may not make any sense because I don't understand this. But here it is:
But that is incorrect.