Answer
$\dfrac{364}{2187}$
Work Step by Step
The general formula to find the nth partial sum of a Geometric sequence is given as: $ S_{n}=\dfrac{a(1-r^n)}{(1-r)}$
$ a_1=(\dfrac{1}{3})^{1+1}=\dfrac{1}{9}$ for $ i=1$
Now, $ S_{6}=\dfrac{(\dfrac{1}{9}) \times [1-(\dfrac{1}{3})^{6}]}{[1-(\dfrac{1}{3})]}=\dfrac{1}{9} \times (\dfrac{364}{243})$
Our answer is: $ S_{6}=\dfrac{364}{2187}$
