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

The sum of this series is undefined (it alternates tending towards $+ \infty$ and $- \infty$)
The sum of an infinite geometric series only exists if the geometric ratio, $r$ is such that $\left\mid r \right\mid < 1$
In this case the geometric ratio is $\frac{- 12}{3} = - 4$