This formula applies to fermionic systems as well as bosonic systems. Fermi–Dirac statistics arises when considering the effect of the Pauli exclusion principle : whilst the number of fermions occupying the same single-particle state can only be either 1 or 0, the number of bosons occupying a single particle state may be any integer. Thus, the grand partition function for bosons can be considered a geometric series and may be evaluated as such: Z = ∑ ∑ N = 0 ∞ ∞ exp ⁡ ⁡ ( N ( μ μ − − ε ε ) / k B T ) = ∑ ∑ N = 0 ∞ ∞ [ exp ⁡ ⁡ ( ( μ μ − − ε ε ) / k B T ) ] N = 1 1 − − exp ⁡ ⁡ ( ( μ μ − − ε ε ) / k B T ) .