An algebra problem by Ooi Ming Yang

Let the expression be S, where $S= \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...$

Multiply both side by 2, we get

$2S=1+\frac{1}{2}+\frac{1}{4}+...$

Subtract both side by S, we get

$2S-S=1+\frac{1}{2}+\frac{1}{4}+...-(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...)$

$\boxed{S=1}$

It forms infinite GP with $r = \frac {1}{2}$ and $a = \frac {1}{2}$

So $S = \frac {a}{1-r} = \frac {(\frac {1 }{2})}{1-\frac {1}{2}} = 1$