Determine if the geometric series converges or diverges. If it converges, find its sum.
-$\frac { 1 } { 6 } + \left( \frac { 1 } { 6 } \right) ^ { 2 } + \left( \frac { 1 } { 6 } \right) ^ { 3 } + \left( \frac { 1 } { 6 } \right) ^ { 4 } + \left( \frac { 1 } { 6 } \right) ^ { 5 } + \ldots$
A) converges, $\frac { 1 } { 5 }$
B) diverges
C) converges, $\frac { 6 } { 5 }$
D) converges, $\frac { 5 } { 6 }$

Question

Quizplus · Accepted Answer

The series is a geometric series with $r = \frac { 1 } { 6 } < 1$, so it converges. The sum of a convergent geometric series is given by $S = \frac { a } { 1 - r }$, where $a$ is the first term and $r$ is the common ratio. In this case, $a = \frac { 1 } { 6 }$ and $r = \frac { 1 } { 6 }$, so the sum is $S = \frac { \frac { 1 } { 6 } } { 1 - \frac { 1 } { 6 } } = \frac { 1 } { 5 }$.

Determine If the Geometric Series Converges or Diverges A) Converges 15\frac { 1 } { 5 }51​

Determine If the Geometric Series Converges or Diverges A) Converges $\frac { 1 } { 5 }$