Question

The sum of infinite terms of the following series $1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+..$ will be

• A. $\frac{3}{16}$
• B. $\frac{25}{8}$
• C. $\frac{35}{4}$
• D. $\frac{35}{16}$

Answer 1

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

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

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

$S-\frac{1}{5}S=1+\frac{3}{5}+\frac{3}{5^2}+\frac{3}{5^3}+..$

$\frac{4}{5}S=1+3(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+..)$

$=1+3\times \frac{\frac{1}{5}}{1-\frac{1}{5}}$

$\frac{4}{5}S=\frac{7}{4}$

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