Thread: Pre-Exam Calculus Questions

I will be glad to get some guidance to the following questions:

1. Determine whether the next series converges , diverges or absolutely converges:
.

2. Find all the values of the parameters a,b which for these values the integral converges:
.

Thanks in advance... I'll show what I've tried in the reply.

About the first one:

If we take this series from n=3 in absolute value, we can say it's less than:

All I need is to show that the series above converges...The problem is that the number of conjunct elements depends on n...

The second one:
The only problematic point is 0 ... We can substitute or something, but I don't think it's necessary ... Because we can say it's less than ... I can't figure out how to use now something like the comparison test... There must be an easy way...

About the third one- I've no idea


Thanks a lot!