# How do you find the sum of the infinite geometric series 100+90+81+72.9+65.61...?

The sum of the infinite geometric series is $1000$.
This is a geometric series with first term as $100$ and ratio of a term to its preceding term as $\frac{90}{100} = 0.9$. As this ratio is less than $1$, the sum of the infinite geometric series is
$\frac{100}{1 - 0.9} = \frac{100}{0.1} = 100 \times 10 = 1000$