Well, seeing as b is a constant, that implies that as m goes through the different values, from one to infinity, b is unaffected. So, what can we do with it?
EDIT: If it isn't immediately evident why b remains unaffected as m goes through its different values, and what we can do with it, let's calculate a partial sum of this series. Let's find the sum for just $\displaystyle m=1,2,~and~3$
$\displaystyle \frac{e^{-a \cdot (1)^2}}{b \cdot (1)^2} + \frac{e^{-a \cdot (2)^2}}{b \cdot (2)^2} + \frac{e^{-a \cdot (3)^2}}{b \cdot (3)^2} $
What do you notice about "a" and "b," as m goes from 1 to 3?