A geometry problem by Soham Chitnis

$\frac{9}{2} + \frac{9}{8} + \frac{9}{32} + \frac{9}{128} + ...$

This is the sum of a geometric series with first term $a = \frac{9}{2}$ and common ratio $r = \frac{1}{4}$ .

The sum of an infinite geometric series with $|r|<1$ is $S_{\infty} = \frac{a}{1 - r} = \frac{\frac{9}{2}}{1 - \frac{1}{4}} = \frac{9}{2}\cdot\frac{4}{3} = 6$ , giving an answer of option A i.e 6