## College Algebra (10th Edition)

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