Find the sum to infinity of the following s..

Question 1 Report

Find the sum to infinity of the following series. 0.5 + 0.05 + 0.005 + 0.0005 + .....

\frac{5}{8}

\frac{5}{7}

\frac{5}{11}

\frac{5}{9}

Answer Details

Using S $\infty$ = $\frac{a}{1 - r}$
r = $\frac{0.05}{0.5}$ = $\frac{1}{10}$
S $\infty$ = $\frac{0.5}{\frac{1}{10}}$

= $\frac{0.5}{(\frac{9}{10})}$
= $\frac{0.5 \times 10}{9}$
= $\frac{5}{9}$