1. ## generating functions problem

can you help for this question please ? I try to solve but its hard for me

2. Hello,

The first 2 are correct.

For the 3rd one :

$\frac{x^2}{1-x^2}=x^2\cdot\frac{1}{1-x^2}=\frac{x^2}{2}\cdot\left(\frac{1}{1-x}+\frac{1}{1+x}\right)$

But $\frac{1}{1-x}+\frac{1}{1+x}=\sum_{n=0}^\infty x^n+\sum_{n=0}^\infty (-1)^n x^n=\sum_{n=0}^\infty a_n x^n$

where $a_n=\begin{cases} 2 \text{ if n is even} \\ 0 \text{ if n is odd}\end{cases}$

Can you finish it ?