Chapter 9.4, Problem 50E

Using a Series Consider the series ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{1}{{(n+2)}^2}}$.

(a) Verify that the series conserves.

(b) Use a graphing utility to complete the table

n	5	10	20	50	100
$S_n$.

(c) The sum of the series is $({\pi }^2/6)-(5/4)$. Find the sum of the series

${\displaystyle \underset{n=6}{\overset{\infty }{\sum }}\frac{1}{{(n+2)}^2}}$

(d) Use a graphing utility to find the sum of the series

${\displaystyle \underset{n=15}{\overset{\infty }{\sum }}\frac{1}{{(n+2)}^2}}$