# How do you find the sum of the convergent series 3-9+27-81+... If the convergent series is not convergent, how do you know?

Dec 21, 2015

The series $3 , - 9 , + 27 , - 81 , \ldots$
has a ratio of $r = \left(- 3\right)$ (i.e. ${a}_{i + 1} = {a}_{i} \times \left(- 3\right)$ )
$\textcolor{w h i t e}{\text{XXX}} \left\mid r \right\mid < 1$