Test for convergence $\sum_{n=1}^{\infty} \frac{1}{2^\sqrt{n}}$ Possible Duplicate:
  convergence of a series involving $x^\sqrt{n}$  




Test for convergence
$$\sum_{n=1}^{\infty} \frac{1}{2^\sqrt{n}}$$
My first thought was to use the ratio test but it's inconclusive since it yields $1$.
Are there some easy means to test the sum for convergence? Thanks!
Hint: For $n&gt;2^{10}$, we have that $$\sqrt{n}\geq 2\log_2(n),$$  and so for $n&gt;2^{10}$ $$2^{\sqrt{n}}\geq n^2.$$  Now try using the comparison test.
So, you could use the comparison test, that one would yield results.