The "hard part", of course, is that infinite sum.
Let \(\displaystyle S= \frac{1}{5}+ \frac{1}{5^2}+ \frac{1}{5^3}+ \cdot+ \cdot+ \cdot+ \frac{1}{5^n}+ \cdot\cdot\cdot\)
Factor out \(\displaystyle \frac{1}{5}\):
\(\displaystyle S= \frac{1}{5}\left(1+ \frac{1}{5}+ \frac{1}{5^2}+ \cdot+ \cdot+ \cdot+ \frac{1}{5^{n-1}}+ \cdot\cdot\cdot\right)\).
Do you see that, after the "1+ " the sum on the right is just the original sum, with the index shifted? And since the sum is infinite, that is just the original "S"!
\(\displaystyle S= \frac{1}{5}(1+ S)\).
So \(\displaystyle 5S= 1+ S\), \(\displaystyle 4S= 1\), and \(\displaystyle S= \frac{1}{4}\).
Add 2 to that.