Question

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

• A. $\frac{16}{35}$
• B. $\frac{11}{8}$
• C. $\frac{35}{16}$
• D. $\frac{17}{6}$

Answer 1

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

Let $S=1+4x+7x^2+10x^3+........$
then $xS=x+4x^2+7x^2+..........$
$\Rightarrow S(1-x)=1+3(x+x^2+x^3+......)$
Here $x=\frac{1}{5}$
put $x=\frac{1}{5}$ , we get $S=\frac{35}{16}$