Question

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

Answer 1

`oo`. The series is divergent since `|r|>1`.

Explanation:

For any infinite geometric series of form `sum_(n=1)^ooar^(n-1)`, the sum is given by `a/(1-r)` if and only if `|r|<1`.

In this case, `r=x_(n+1)/x_n=5/4>1` and so this implies that the series does not converge and has no finite sum.