Use the Formula for the Sum of an Infinite Geometric Series
-$3 - 1 + \frac { 1 } { 3 } - \frac { 1 } { 9 } + \ldots$
A) $\frac { 9 } { 4 }$
B) 2
C) $- 1$
D) does not exist

Question

Quizplus · Accepted Answer

The given series is an infinite geometric series with the first term $a = 3$ and common ratio $r = -\frac{1}{3}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$ when $|r| < 1$. Substituting $a = 3$ and $r = -\frac{1}{3}$, we get $S = \frac{3}{1 - (-\frac{1}{3})} = \frac{3}{\frac{4}{3}} = \frac{9}{4}$.

Use the Formula for the Sum of an Infinite Geometric 3−1+13−19+…3 - 1 + \frac { 1 } { 3 } - \frac { 1 } { 9 } + \ldots3−1+31​−91​+…

Use the Formula for the Sum of an Infinite Geometric $3 - 1 + \frac { 1 } { 3 } - \frac { 1 } { 9 } + \ldots$