Find the sum of the series.
-$$\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 5 } { 9 ^ { n } }$$
A) $\frac { 9 } { 2 }$
B) $\frac { 5 } { 8 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 45 } { 8 }$

Question

Quizplus · Accepted Answer

The sum of an infinite geometric series is given by the formula:$$\sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}$$where $a$ is the first term and $r$ is the common ratio. In this case, $a = -5/9$ and $r = -1/9$, so the sum of the series is:$$\sum_{n=0}^{\infty} \left(-\frac{5}{9}\right) \left(-\frac{1}{9}\right)^n = \frac{-\frac{5}{9}}{1-\left(-\frac{1}{9}\right)} = \frac{-\frac{5}{9}}{\frac{10}{9}} = -\frac{1}{2}$$

Find the Sum of the Series ∑n=0∞(−1)n59n\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 5 } { 9 ^ { n } }n=0∑∞​(−1)n9n5​

Find the Sum of the Series $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 5 } { 9 ^ { n } }$