The problem is to solve f_{a}(x)=(x-1)^{-2}.

The textbook told me to assume a_{n}= (c_{1}n+c_{2})1^{n}.

So from (x-1)^{-2}=c_{1}x/(1-x)^{-2}+c_{2}x/(1-x) (using generating functions for $\displaystyle \sum nx^n$ and $\displaystyle \sum x^n$, I got the equation 1=c_{1}x+c_{2}x(1-x).

But I'm stuck, since the right hand side involves no constant terms.

The textbook says I'm supposed to get n+1.

How can I proceed from the assumption a_{n}= (c_{1}n+c_{2})1^{n}?