Question

Find the sum to infinity of the $G.P\frac{1}{2}+\frac{1}{4}+\frac{1}{8}$ +........

Answer 1

$S_{\infty }=\frac{a_1}{1-r}r=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}$
$\frac{\frac{1}{2}}{1-\frac{1}{2}}=\frac{\frac{1}{2}}{\frac{1}{2}}\Rightarrow 1=1$