# How do you find the sum of the infinite geometric series 50 + 125/2 + 625/8 + 3125/32?

$\infty$. The series is divergent since $| r | > 1$.
For any infinite geometric series of form ${\sum}_{n = 1}^{\infty} a {r}^{n - 1}$, the sum is given by $\frac{a}{1 - r}$ if and only if $| r | < 1$.
In this case, $r = {x}_{n + 1} / {x}_{n} = \frac{5}{4} > 1$ and so this implies that the series does not converge and has no finite sum.