In class we have shown that

X

n$=0$

$1$

n$2+$ a$2=$

$2$a

$1$

tanh$($a$)+1$

$2$a$2$

$.$

Use similar approach to calculate the infinite sums in this problem.

$($a$)$ Calculate

S $=$

n$=$X

n$=0$

$1$

$($n$2+$ a$2)2.$

$($b$)$ Show that X

n$=1$

$1$

n$3$ tanh$($n$)=7$

$180$$2.$