Evaluate:
$\displaystyle \frac{1}{2}+\frac{1}{4}+\frac{1}{4}+\frac{3}{16}+\ frac{5}{32}...$
I know the formula for an infinite series:
$\displaystyle \frac{a}{1-r}$
But i cannot seem to find the rate. I have tried grouping the terms, and doing two infinite series, but I still cannot find a pattern. Any help is appreciated.