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

• Jun 12th 2013, 11:26 AM
kicma
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
• Jun 12th 2013, 11:52 AM
Plato
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.
• Jun 13th 2013, 03:10 AM
kicma
Re: Series 1/(2^(sqrt(n))
I know that but I have a problem finding series to compare to.
• Jun 13th 2013, 03:34 AM
Plato
Re: Series 1/(2^(sqrt(n))
Quote:

Originally Posted by kicma
I know that but I have a problem finding series to compare to.

HINT: ${\lim _{n \to \infty }}\frac{{{n^2}}}{{{2^{\sqrt n }}}} = ?$
• Jun 13th 2013, 05:56 AM
kicma
Re: Series 1/(2^(sqrt(n))
Thanks, I got it.