Question

value from 1/5 + 1/25 + 1/625 + ...

Answer 1

use
\[S=\frac{a}{1-r}\] with \(a=r=\frac{1}{5}\)

Answer 2

you can almost do it in your head
"one minus one fifth is four fifths"
and
"one fifth divided by four fifths is one fourth"