# Expansion of Bose Distribution at low Temperatures [closed]

I have a phononic system with its distribution

$$N_B(E,T) = \frac{1}{e^{E/k_BT}-1}$$

where $E$ is the energy and $T$ the temperature of the system.

I'd like to know how to make an expansion of this at low temperatures, that is $$E>>k_B T$$

Hint: Multiply both the numerator and the denominator by $e^{-E/k_BT}$ to get
$$N_B(E,T) = \frac{1}{e^{E/k_BT}-1}=e^{-E/k_BT}\cdot \frac{1}{1-e^{-E/k_BT}}$$
This gives you something that looks like $\dfrac{1}{1-x}$ which can be expanded for $|x|<1$.