Answer
$1+\displaystyle \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\cdots+\frac{1}{3^{n}}$
Work Step by Step
We see that there are $n+1$ terms, as the index $k$ changes from $0$ to $n$. The index $k$ indicates how the terms are formed.
We write out the sum for the terms as follows:
$\displaystyle \sum_{k=0}^{n}\frac{1}{3^{k}}=\frac{1}{3^{0}}+\frac{1}{3^{1}}+\frac{1}{3^{2}}+\frac{1}{3^{3}}+...+\frac{1}{3^{n}} \\=1+\displaystyle \frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{3^{n}}$
