Investigate the convergence of:
.
So I broke it down into:
I have no idea how to write this as the nth partial sum. I tried writing the first few terms:
I'm completely lost. Thanks!
Ah, I think I get it. So using in the first problem (since this when terms begin to cancel each other out) you eventually arrive at:
and then simply substitute in the denominators and I get what you got.
So for the second problem I posted, is this correct?
and thus leading to: