Answer
$\approx 4.9986$
Work Step by Step
We have to compute the sum of the geometric sequence:
$2+\dfrac{6}{5}+\dfrac{18}{25}+...+2\left(\dfrac{3}{5}\right)^{15}$
The sum can be written as:
$\sum_{n=1}^{16} 2\left(\dfrac{3}{5}\right)^{n-1}$
The elements of the geometric sequence are:
$a_1=2$
$r=\dfrac{3}{5}$
$n=16$
Use a graphing utility to find the sum of the geometric sequence:
$sum\left(seq\left(2\left(\dfrac{3}{5}\right)^{n-1},n,1,16\right)\right)\approx 4.99858944505\approx 4.9986$
