Question

The sum of the series $1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\dots \infty$ is

• A. 7/16
• B. 5/16
• C. 105/64
• D. 35/16

Answer 1

Answer: (D)

35/16

Let,

$S=1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+\dots \infty$

Then,

$\frac{1}{5}S=\frac{1}{5}+\frac{4}{5^2}+\frac{7}{5^3}+\dots \infty$

$\Rightarrow S(1-\frac{1}{5})=1+3[\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+\dots \infty ]$

$\Rightarrow \frac{4}{5}S=1+3\times \frac{1/5}{1-\left(1/5\right)}=1+\frac{3}{4}=\frac{7}{4}$

$\Rightarrow S=\frac{35}{16}$