Sum of an infinite geometric series

Statement

Compute the sum of the infinite geometric series $5 + 5\cdot\frac{1}{4} + 5\cdot\left(\frac{1}{4}\right)^{2} + 5\cdot\left(\frac{1}{4}\right)^{3} + \dots$

Solution

It is a geometric series with first term $a = 5$ and ratio $q = \dfrac{1}{4}$, with $|q| < 1$; it converges to the sum $S = \frac{a}{1-q} = \frac{5}{1 - \frac{1}{4}} = \frac{5}{\frac{3}{4}} = \boxed{\frac{20}{3} \approx 6{.}67}.$