### Home > PC > Chapter 7 > Lesson 7.3.2 > Problem7-107

7-107.

Does Austin’s method work on an alternating geometric series? Try the method on the following series: $1 − 3 + 9 − 27 + 81 − 243 + 729 − 2187$

Multiply $S$ by $3$ and ADD the two series. What happens?

$S = 1 − 3 + 9 − 27 + 81 − 243 + 729 − 2187$
$3S = + 3− 9 + 27 − 81 + 243 − 729 + 2187 − 6561$

So…
$3S + S = + 1 − 6561$
$4S = −6560$

$S = −1640$