Let $S=\sum\limits_{n=1}^\infty a_n$ be an infinite series such that $S_N=3-\frac{6}{N^2}$.

(a) What are the values of $\sum\limits_{n=1}^{10} a_n$ and $\sum\limits_{n=4}^{16} a_n$?
$\sum\limits_{n=1}^{10} a_n=$
$\sum\limits_{n=4}^{16} a_n=$

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

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

(d) Find the sum $\sum\limits_{n=1}^\infty a_n$.
$\sum\limits_{n=1}^\infty a_n=$