Answer
See below.
Work Step by Step
The sum of a geometric sequence until $n$ can be obtained by the formula $S_n=a_1(\frac{1-r^n}{1-r})$ where $a_1=\frac{1}{3}$ is the first term and $r=\frac{1}{3}$ is the common ratio. Hence here the sum is: $S_n=\frac{1}{3}(\frac{1-(\frac{1}{3})^7}{1-\frac{1}{3}})=\frac{1093}{2187}\approx0.49977$.
