Question

Let $S=1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\dots \infty$, then the value of $S$ is

• A. $\frac{29}{8}$
• B. $\frac{33}{16}$
• C. $\frac{35}{16}$
• D. $\frac{25}{4}$

Answer 1

The correct option is C $\frac{35}{16}$

$S=1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\dots$
This is AGP with $a=1,r=\frac{1}{5},d=3$
$S=\frac{a}{1-r}+\frac{d\cdot r}{(1-r{)}^2}$
$=\frac{1}{1-\frac{1}{5}}+\frac{3\times \frac{1}{5}}{{(1-\frac{1}{5})}^2}$
$=\frac{35}{16}$