Sum of series $\sum_{n=0}^{+\infty}\frac{1}{e^{\beta n}+1}$ with $\beta >0$

Question

I'm wondering if there exists a closed form or at least some asymptotic expansion in the limit $\beta \rightarrow \infty$ for the sum of the series $$\sum_{n=0}^{+\infty}\frac{1}{e^{\beta n}+1}$$ with $\beta >0$.

$1/(e^{\beta n}+1)$ is the Fermi distribution $1/(e^{\beta (\epsilon_n-\mu)}+1)$ with chemical potential $\mu=0$ and energy $\epsilon_n=n$.