How do I show that P[X=k+1] = [p/(1-p)][(n-k)/k+1)]P[X=k]

Also, how do I prove that as k goes from 0 to n, P[X=k] first increases and then decreases, with it reaching largest value when k is the largest integer less than or equal to (n+1)p.

Thanks!

I have no idea how to even start this problem