Oh Mr. Fantastic I should've asked you this earlier...I was just soo excited someone actually replied to my post... you see i haven't had much help for a while on mathhelp...but any who. how did you know to compare that sum with ?Now note:
1. .
So the first sum converges by the comparison test.
I believe you've used the comparison test, again, after finding out converges by the ratio test? Similarly, how did you know to use2. and converges by the ratio test.
So the second sum converges.
Thank you Mr. Fantastic
In both cases it's a matter of guessing whether the series is convergent or divergent and then trying to construct an appropriate series to use in the comparison. The key is a lot of practice to develop experience - after a while you get to 'see' (sometimes) what the series will be that you need to use.