Answer
$2,391,484.\bar{3}$
Work Step by Step
We have to compute the sum of the geometric sequence:
$\dfrac{3}{9}+\dfrac{3^2}{9}+\dfrac{3^3}{9}+...+\dfrac{3^{15}}{9}$
The elements of the geometric sequence are:
$a_1=\dfrac{3}{9}=\dfrac{1}{3}$
$r=3$
$n=15$
The sum can be written:
$\sum_{n=1}^{15}\dfrac{1}{3}(3^{n-1})=\sum_{n=1}^{15}3^{n-2}$
Use a graphing utility to find the sum of the geometric sequence:
$sum\left(seq\left(3^{n-2},n,1,15\right)\right)=2,391,484.\bar{3}$
