The possible particle energies of a system of particles are 0, , 2, . . . n

The possible particle energies of a system of particles are 0, є, 2є, . . . nє . . . 

a. Show that the partition function of the system (with gi = 1) is

Z = (1 - e-є/kT)-1

b. Compute the average energy of the particles.

c. Find the limiting value of the average energy when є is much smaller that kT.