Determine if the geometric series converges or diverges. If it converges, find its sum.
-$$1 + ( - 9 ) + ( - 9 ) ^ { 2 } + ( - 9 ) ^ { 3 } + ( - 9 ) ^ { 4 } + \ldots$$
A) converges, 9
B) diverges
C) converges, 90
D) converges, 81

Question

Quizplus · Accepted Answer

The series diverges because the common ratio $r = -9$ has an absolute value greater than 1 ($|r| > 1$), which means the series does not converge to a finite sum.

Determine If the Geometric Series Converges or Diverges 1+(−9)+(−9)2+(−9)3+(−9)4+…1 + ( - 9 ) + ( - 9 ) ^ { 2 } + ( - 9 ) ^ { 3 } + ( - 9 ) ^ { 4 } + \ldots1+(−9)+(−9)2+(−9)3+(−9)4+…

Determine If the Geometric Series Converges or Diverges $1 + ( - 9 ) + ( - 9 ) ^ { 2 } + ( - 9 ) ^ { 3 } + ( - 9 ) ^ { 4 } + \ldots$