Answer
$8191.75$
Work Step by Step
We have to compute the sum of the geometric sequence:
$\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{2^2}{4}+...+\dfrac{2^{14}}{4}$
The elements of the geometric sequence are:
$a_1=\dfrac{1}{4}$
$r=2$
$n=15$
The sum can be written as:
$\sum_{n=0}^{14}\dfrac{1}{4}(2^n)$
Use a graphing utility to find the sum of the geometric sequence:
$sum\left(seq\left(\dfrac{1}{4}(2^n),n,0,14\right)\right)=8191.75$
