# Math Help - Series 1/(2^(sqrt(n))

1. ## Series 1/(2^(sqrt(n))

sum (1/(2^(sqrt(n)))) from 1 to infinity - Wolfram|Alpha

I need to prove that this series converges. Thanks

2. ## Re: Series 1/(2^(sqrt(n))

This is a special case of the limit comparison test.

If each of $\sum {{a_n}} \;\& \;\sum {{b_n}}$ is a series of positive terms and $\sum {{b_n}}$ converges and if ${\lim _{n \to \infty }}\frac{{{a_n}}}{{{b_n}}} = 0$ then $\sum {{a_n}}$ also converges.

3. ## Re: Series 1/(2^(sqrt(n))

I know that but I have a problem finding series to compare to.

4. ## Re: Series 1/(2^(sqrt(n))

Originally Posted by kicma
I know that but I have a problem finding series to compare to.
HINT: ${\lim _{n \to \infty }}\frac{{{n^2}}}{{{2^{\sqrt n }}}} = ?$

5. ## Re: Series 1/(2^(sqrt(n))

Thanks, I got it.