Prove that the nth energy level of atom has degeneracy n^2

[tententententen]

Homework Statement

Prove that the nth energy level of an atom has degeneracy equal to n^2.

Homework Equations

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.

 

[mfb]

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?

Something along that line I guess.
I guess you can use the rules for allowed l and m and don't have to derive them?