How do you find the sum of the infinite geometric series 405 + 270 + 180...?

The sum is $1215$

Explanation:

We need to find the common ratio of the series which is

$r = \frac{270}{405} = \frac{2}{3}$

hence the sum of the infinite series is given by

$S = \frac{{a}_{1}}{1 - r} = \frac{405}{1 - \frac{2}{3}} = 1215$

where ${a}_{1}$ is the first term of the series.