Determine whether the infinite geometric series converges. If the series converges, determine the limit.
-$$36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots$$
A) Diverges
B) Converges; - 5616
C) Converges; 45
D) Converges; 30

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 36$ and common ratio $r = \frac{1}{5}$. Since $|r| < 1$, the series converges. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, so substituting $a = 36$ and $r = \frac{1}{5}$ gives $S = \frac{36}{1 - \frac{1}{5}} = \frac{36}{\frac{4}{5}} = \frac{36 \times 5}{4} = 45$.

Determine Whether the Infinite Geometric Series Converges 36+365+3625+36125+…36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots36+536​+2536​+12536​+…

Determine Whether the Infinite Geometric Series Converges $36 + \frac { 36 } { 5 } + \frac { 36 } { 25 } + \frac { 36 } { 125 } + \ldots$