Use the Formula for the Sum of an Infinite Geometric Series
-$$\frac { 1 } { 3 } - 1 + 3 - \ldots$$
A) $\frac { 1 } { 12 }$
B) 2187
C) $- 729$
D) does not exist

Question

Quizplus · Accepted Answer

The formula for the sum of an infinite geometric series is $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. For the series to converge, $|r| < 1$. In this series, the first term $a = \frac{1}{3}$ and the common ratio $r = -3$. Since $|r| = 3 > 1$, the series does not converge, and thus the sum does not exist.

Use the Formula for the Sum of an Infinite Geometric 13−1+3−…\frac { 1 } { 3 } - 1 + 3 - \ldots31​−1+3−…

Use the Formula for the Sum of an Infinite Geometric $\frac { 1 } { 3 } - 1 + 3 - \ldots$