How would one do the following

[praharmitra]

How would one do the following sum?

<br /> <br /> \sum\limits_{n=1}^\infty n e^{- \epsilon~n^2}<br /> <br />

 

[SteamKing]

First of all, find out what epsilon is.

 

[Simon Bridge]

How would one do the following sum?

...carefully. What have you tried?

note $$\frac{d}{dn}e^{-\epsilon n^2}=-2\epsilon ne^{-\epsilon n^2}$$ ... may or may not be helpful.