How do i show from the Legendre's Polynomial equation $$P\_n(x)=\sum\_{k=0}^N \dfrac{(-1)^k(2n-2k)!}{2^nk!(n-k)!(n-2k)!}x^{n-2k}$$ where $N=n/2$ for even $n$ and $ N=(n-1)/2$ for odd $n$. Using just this information how to show $P\_n(1)=1$?
Can somebody hint?