I ignored your Taylor work, but I tested your idea
I just tried the limit comp test with
By that, I mean
So, is a positive series and it can be compared to the p=2 series.
, convergent or divergent?
Now using the Taylor expansion of with AND using the taylor expansion of I got
To be able to use the comparison critera, , I applied it with on
So the original series converges.
I assume if then ?
Basically what I want, is someone to check the work.