Calculating Total Energy and Number of States for N Harmonic Oscillators

[basma]

I am having this problem in my book:

For a set of N identical harmonic oscillators, the energy for the ith harmonic oscillator is E(i)= (n(i) - 1/2)*h (nu).
(a) What is the total energy of this system?
(b) What is the number of states, Omega (E) , for N=2 and 3?
(c) What is the number of states for a large N.

I thought about the first part. I think I should just add all these energies.

Basma

 

[basma]

Any help would be appreciated. I can't even start this problem.

Thanks