Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-$$- 30 - 5 - \frac { 5 } { 6 } - \cdots$$
A) Converges; $- 30$
B) Converges; 6
C) Converges; $- 36$
D) Converges; $- \frac { 215 } { 6 }$

Question

Quizplus · Accepted Answer

The series converges because the common ratio $ r = \frac{-5/6}{-5} = \frac{1}{6} $ is between -1 and 1. The sum of an infinite geometric series is given by $ S = \frac{a}{1-r} $, where $ a = -30 $ and $ r = \frac{1}{6} $. Thus, $ S = \frac{-30}{1 - \frac{1}{6}} = -36 $.

Determine Whether the Infinite Geometric Series Converges or Diverges −30−5−56−⋯- 30 - 5 - \frac { 5 } { 6 } - \cdots−30−5−65​−⋯

Determine Whether the Infinite Geometric Series Converges or Diverges $- 30 - 5 - \frac { 5 } { 6 } - \cdots$