Evaluate the series, if it converges.
-$3 - 2 + \frac { 4 } { 3 } - \frac { 8 } { 9 } + \ldots$
A) $\frac { 3 } { 5 }$
B) Does not converge
C) $- \frac { 6 } { 5 }$
D) $\frac { 9 } { 5 }$

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 3$ and common ratio $r = -\frac{2}{3}$. Since $|r| < 1$, the series converges to $\frac{a}{1-r} = \frac{3}{1 - (-\frac{2}{3})} = \frac{3}{\frac{5}{3}} = \frac{9}{5}$.

Evaluate the Series, If It Converges 3−2+43−89+…3 - 2 + \frac { 4 } { 3 } - \frac { 8 } { 9 } + \ldots3−2+34​−98​+…

Evaluate the Series, If It Converges $3 - 2 + \frac { 4 } { 3 } - \frac { 8 } { 9 } + \ldots$