Evaluate the series, if it converges.
-$$9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots$$
A) Does not converge
B) $\frac { 15 } { 2 }$
C) $\frac { 5 } { 6 }$
D) $- \frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

This series is a geometric series with the first term $a = 9$ and common ratio $r = -\frac{1}{5}$. The sum of a convergent geometric series is given by $S = \frac{a}{1 - r}$. Substituting the given values, we get $S = \frac{9}{1 - (-\frac{1}{5})} = \frac{9}{1 + \frac{1}{5}} = \frac{9}{\frac{6}{5}} = \frac{9 \times 5}{6} = \frac{45}{6} = \frac{15}{2}$.

Evaluate the Series, If It Converges 9−95+925−9125+…9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots9−59​+259​−1259​+…

Evaluate the Series, If It Converges $9 - \frac { 9 } { 5 } + \frac { 9 } { 25 } - \frac { 9 } { 125 } + \ldots$