The sum to infinity of the series 1+45+752+1053+… 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)

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

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