Q:

Series: Let $S=\sum\limits_{n=1}^\infty a_n$ be an infinite series such that $S_N=4-\frac{2}{N^2}$.

Let $S=\sum\limits_{n=1}^\infty a_n$ be an infinite series such that $S_N=4-\frac{2}{N^2}$.
(a) Find a general formula for $a_n$. 
(b) Find the sum $\sum\limits_{n=1}^\infty a_n$. 
Can you explain to me how I can convert the partial sum to the general equation?
(a) What are the values of
$\sum\limits_{n=1}^{10} a_n$ and $\sum\limits_{n=4}^{16} a_n$?
$\sum\limits_{n=1}^{10} a_n=23433271/635040$
$\sum\limits_{n=4}^{16} a_n= 15799025474051/259718659200 $
(b) What is the value of $a_3$?
$167/18$
Why aren't these values correct as well?

A:

Here are some hints.
(a) You make $S_n$ by adding $a_n$ to $S_{n-1}$.
(b) What is the definition of $\sum_{n=1}^\infty a_n$?

