### Home > APCALC > Chapter 9 > Lesson 9.1.2 > Problem9-30

9-30.

CALCULATING PARTIAL SUMS FOR AN INFINITE GEOMETRIC SERIES

We can use the method for determining the sum of an infinite series to calculate finite partial sums. Finish the work below. Your end result should be $S _ { n } = \frac { a - a r ^ { n } } { 1 - r }$.

$\left. \begin{array} \\ { S _ { n } = a + a r + a r ^ { 2 } + \ldots + a r ^ { n - 1 } } \\ { r S _ { n } = \quad a r + a r ^ { 2 } + \ldots + a r ^ { n - 1 } + a r ^ { n } } \end{array} \right.$

$S_n-rS_n=a+ar^n$

Factor the left side of the equation.