Expand and derive the planck occupanncy

[Howlin]

Homework Statement

The average energy of a harmonic oscillator is written using Boltzmann statistics as:

<ε> = (<n> +.5) = $\frac{\sum_{n} ε_{n} exp \frac{-ε_{n}}{kt}}{\sum_{n} exp \frac{-ε_{n}}{kt}}$

Expand the expontentials and hence derive the Planck Occupancy
<n> = n(ω,T) =$\frac{1}{exp\frac{h bar * ω}{kT}-1}$

Homework Equations

The two are above in part 1

The Attempt at a Solution

I have not been able to even start this question as I cannot understand what is meant by the expand the exponentials. Any help to start this off would be greatfull and as I have been stuck on this for nearly an hour.
Thank you

 

[Fightfish]

Basically, it is asking you to evaluate the sums.