# How do you find the sum of the infinite geometric series Sigma -3(0.9)^n from n=0 to oo?

Jun 18, 2017

$S = {\sum}_{n = 0}^{\infty} - 3 {\left(0.9\right)}^{n} = - 30$

#### Explanation:

The sum:

$S = {\sum}_{n = 0}^{\infty} - 3 {\left(0.9\right)}^{n}$

represents a GP with $a = - 3$ an $r = 0.9$ so as $| r | < 1$we can use the standard GP summation result:

${s}_{\infty} = \frac{a}{1 - r}$

Which gives us:

$S = \frac{- 3}{1 - 0.9}$
$\setminus \setminus = \frac{- 3}{0.1}$
$\setminus \setminus = - 30$