\(\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ...\)

The expression above can be determined as the sum of an infinite geometric series

Each term can be written as \(1*(\frac{1}{5})^n\)

Using this information, we can plug the values into the formula for the sum of an infinite geometric series

\(\frac{\frac{1}{5}}{1 - \frac{1}{5}} = \frac{1}{4}\)

Finally we get an answer of 1/4

:D