Find the value $P_n(1)$ of the Legendre polynomials from their generating function

Question

Here is the question:

Using $\sum_{n=0}^{\infty}P_n(x)r^n=(1-2rx+r^2)^{-\frac{1}{2}}$ find the value of $P_n(1)$

I am unsure how to handle this question. I did the following and would like clarification on if it is correct or how to correct it if not.

$\sum_{n=0}^{\infty}P_n(1)r^n=(1-2r+r^2)^{\frac{-1}{2}}=(r-1)^{-1}$

Not sure where to go from here?

Answer 1

Since $1/(1-r)=\sum_{n=0}^\infty r^n$ equating coefficients gives $P_n(1)=1$.