Answer
$1+\displaystyle \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots+\frac{1}{3^{n}}$
Work Step by Step
There are n terms, as the index k changes from 0 to n-1.
The index k dictates how the terms are formed:
$\displaystyle \sum_{k=0}^{n-1}\frac{1}{3^{k+1}}=\frac{1}{3^{0+1}}+\frac{1}{3^{1+1}}+\frac{1}{3^{2+1}}+...+\frac{1}{3^{n-1+1}}$
$=\displaystyle \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\cdots+\frac{1}{3^{n}}$
