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**deezy** Determine if $\displaystyle \sum_{n=0}^{\infty} \frac {(-1)^{n+1}}{n^5+n+6}$ converges absolutely or conditionally. Approximate the sum within an accuracy of 0.01.

$\displaystyle \sum_{n=0}^{\infty} |\frac {(-1)^{n+1}}{n^5+n+6}|$

$\displaystyle \sum_{n=0}^{\infty} \frac {1}{n^5+n+6}$

Basic comparison test with $\displaystyle \sum \frac {1} {n^5}$.

$\displaystyle \sum \frac {1} {n^5}$ converges, so $\displaystyle \sum_{n=0}^{\infty} \frac {1}{n^5+n+6}$ 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?