The estimate for $\sum_{0}^{\infty} e^{-kn^2}-e^{-k(n+1/2)^2}$

Question

I'm trying to give estimate on the following infinite summation:

$\sum_{n=-\infty}^{\infty} (e^{-kn^2}-e^{-k(n+\frac{1}{2})^2})$, and k is some fixed positive number.

The first term in the summation seems to be the $\psi$ function, but I dont know how to deal with the second term.

Thank you advance to anyone who could help.