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

 

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

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

Subtracting (2) from (1), we get 

$\frac{4}{5}S=1+\frac{3}{5}+\frac{3}{5^2}+\frac{3}{5^3}+\dots =1+\frac{3/5}{1-1/5}$

(1)$=1+\frac{3}{4}=\frac{7}{4}$

(2)

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