Use the geometric series formula to find the sum of of $1 + \frac { 1 } { 4 } + \frac { 1 } { 4 ^ { 2 } } + \frac { 1 } { 4 ^ { 3 } } + \frac { 1 } { 4 ^ { 4 } }$
A) $\frac { ( 4 ) ^ { 5 } - 1 } { (4 ) - 1 }$
B) $\frac { \frac {1}{4^5} - 1 } { \frac {1}{4} - 1 }$
C) $\frac { 4 ^ { 4 } - 1 } { 4 - 1 }$
D) $\frac { \frac{1}{4^4} - 1 } { \frac{1}{4} - 1 }$

Question

Use the geometric series formula to find the sum of of  $1 + \frac { 1 } { 4 } + \frac { 1 } { 4 ^ { 2 } } + \frac { 1 } { 4 ^ { 3 } } + \frac { 1 } { 4 ^ { 4 } }$
A) $\frac { ( 4 ) ^ { 5 } - 1 } { (4 ) - 1 }$
B) $\frac { \frac {1}{4^5} - 1 } { \frac {1}{4} - 1 }$
C) $\frac { 4 ^ { 4 } - 1 } {  4 - 1 }$
D) $\frac { \frac{1}{4^4}  - 1 } { \frac{1}{4} - 1 }$

Quizplus · Accepted Answer

The sum of a geometric series is given by $S = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 1$, $r = \frac{1}{4}$, and $n = 5$. Substituting these values into the formula gives $S = \frac{1(1 - (\frac{1}{4})^5)}{1 - \frac{1}{4}}$, which simplifies to the expression in choice B.

Use the Geometric Series Formula to Find the Sum of Of 1