Determine if the geometric series converges or diverges. If it converges, find its sum.
-$$1 + \frac { 1 } { 5 } + \left( \frac { 1 } { 5 } \right) ^ { 2 } + \left( \frac { 1 } { 5 } \right) ^ { 3 } + \left( \frac { 1 } { 5 } \right) ^ { 4 } + \ldots$$
A) converges, $\frac { 5 } { 4 }$
B) diverges
C) converges, $\frac { 7 } { 4 }$
D) converges, 2

Question

Quizplus · Accepted Answer

This is a geometric series with first term 1 and common ratio $\frac{1}{5}$. Since the common ratio is less than 1 in absolute value, the series converges. The sum can be found using the formula $S=\frac{a}{1-r}$ where $a$ is the first term and $r$ is the common ratio, giving $S=\frac{1}{1-\frac{1}{5}}=\frac{5}{4}$. Therefore, the correct choice is (A).

Determine If the Geometric Series Converges or Diverges A) Converges 54\frac { 5 } { 4 }45​

Determine If the Geometric Series Converges or Diverges A) Converges $\frac { 5 } { 4 }$