Determine if converges absolutely or conditionally. Approximate the sum within an accuracy of 0.01.

Basic comparison test with .

converges, so converges as well. The series converges absolutely.

I'm having trouble understanding how to approximate. Do I set up random partial sums until it's less than 0.01? How do I know how how many terms I need for it to be less than 0.01? Is there a formula?