Answer
$\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}$
Work Step by Step
We expand the sigma notation by writing $\frac{1}{i+1}$ as $i$ increases from 1 to 6:
$\displaystyle \sum_{i=1}^{6}\frac{1}{i+1}=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}$
