I've to study this series:
$$\sum_{n=1}^\infty e^{\sqrt n\,x}$$
My teacher wrote that with the asymptotic comparison with this series:
$$\sum_{n=1}^\infty\frac{1}{n^2}$$
My series converges for every
$$x<0$$
I don't understand the motivation, hoping for someone to enlighten me!
=) Thanks. Leonardo.