Is $\sum_{t=1}^{\infty} e^{-\sqrt{t}}$ finite? Is $\displaystyle \sum_{t=1}^{\infty} e^{-\sqrt{t}}$ finite? This is not homework. Actually, a computer algebra package has told me it is finite, but I would like to see a proof. No approach worth trying has occurred to me - a hint would be appreciated...

Do you know that
$$e^{-\sqrt{t}}=_\infty o\left(\frac{1}{t^2}\right)?$$
