Question

Find the sum to infinite terms of a series with $a=\frac{1}{2}andd=\frac{1}{4}$.

Answer 1

$S_{\infty }=\frac{a_1}{1-r}r=\frac{1}{4}-\frac{1}{2}=\frac{\frac{1}{2}}{1+\frac{1}{4}}\Rightarrow \frac{1-2}{4}=\frac{\frac{1}{2}}{\frac{5}{4}}=\frac{1}{2}\times \frac{4}{5}=\frac{2}{5}$