Determine if the infinite geometric series converges or diverges. If the series converges, find its sum.
-$$- 6 - 2 - \frac { 2 } { 3 } - \ldots$$
A) converges, $- \frac { 26 } { 3 }$
B) converges, $- 9$
C) diverges
D) converges, 3

Question

Quizplus · Accepted Answer

The series is geometric with the first term $a = -6$ and common ratio $r = \frac{1}{3}$. Since $|r| < 1$, the series converges. The sum is $S = \frac{a}{1-r} = \frac{-6}{1-\frac{1}{3}} = -9$.

Determine If the Infinite Geometric Series Converges or Diverges −6−2−23−…- 6 - 2 - \frac { 2 } { 3 } - \ldots−6−2−32​−…

Determine If the Infinite Geometric Series Converges or Diverges $- 6 - 2 - \frac { 2 } { 3 } - \ldots$