Let $S={\displaystyle \underset{n=1}{\overset{}{}}}{a}_{n}bean$ infinite series such that $S_N=7-\frac{4}{N^2}.$

$(a)$ 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 $a_n,$ valid for all $n2.$

$a_n=$

$(d)$ Find the sum ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n.(Eligible$ answers include real numbers and the strings "inf", $"-$inf", and "DNE".$)$

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