1. The problem statement, all variables and given/known data Prove that the nth energy level of an atom has degeneracy equal to n^2. 2. Relevant equations 3. The attempt at a solution I was thinking of using the sum from n=1 to N of n = N(N+1)/2 but my professor said i needed to change that equation up a bit to be able to show this. I was also thinking about how l is less than or equal to n-1 and ml is less than l so both of those are sort of n's and together they are n squared? Overall a bit confused.