Solving an infinite series that doesn't seem to be harmonic or geometric

I'm solving a visual problem, and sparing the boring details, I've found the sequence to be:

$\displaystyle {a_n} = \frac{1}{2^{2n-1}}$

I need to solve for the sum of the series from 1 to infinity. Wolfram easily solves this as 2/3. However, I've poured over 2 calculus books and I've enlisted help but we can't solve it by hand.

$\displaystyle \displaystyle\sum_{n=1}^{\infty}\frac{1}{2^{2n-1}}$

Any help at simplifying this into a series which I can solve would be greatly appreciated.