Hello.

I am wondering about this limit

$\displaystyle \mathop {\lim }\limits_{x \to \infty } \sum\limits_{n = - \infty }^{ + \infty } {{{\left( { - 1} \right)}^n}{e^{ - 2{n^2}{x^2}}}} $

The answer is definitely $\displaystyle 1$ since this is related to Kolmogorov distribution which is recognized in statistics field.

But how to prove it?