Problem 65E

65. Use the partial fraction command on your CAS to find a convenient expression for the partial sum, and then use this expression to find the sum of the series. Check your answer by using the CAS to sum the series directly.

$\sum_{n=1}^{\infty} \frac{3 n^{2}+3 n+1}{\left(n^{2}+n\right)^{3}}$

Step-by-Step Solution