Let $S={\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ be an infinite series such that $S_N=8-\frac{6}{N^2}.$

$($a$)$ What are the values of ${\displaystyle \underset{n=1}{\overset{10}{}}}{a}_n$ and ${\displaystyle \underset{n=4}{\overset{16}{}}}{a}_n?$

${\displaystyle \underset{n=1}{\overset{10}{}}}{a}_n=$

${\displaystyle \underset{n=4}{\overset{16}{}}}{a}_n=$

$($b$)$ What is the value of $a_3?$

$a_3=$

$($c$)$ Find a general formula for $a_n.$

$a_n=$

$($d$)$ Find the sum ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n.$

${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n=$

Note: You can earn partial credit on this problem.