Question

How do you find the sum of the infinite geometric series 3 – 12 + 48 – 192 + …?

Answer 1

The sum of this series is undefined (it alternates tending towards `+oo` and `-oo`)

Explanation:

The sum of an infinite geometric series only exists if the geometric ratio, `r` is such that `abs(r) < 1`

In this case the geometric ratio is `(-12)/3=-4`
so the series does not converge and the sum is undefined.