Answer
$\sum\limits_{k=1}^{5}{\frac{k+1}{k+2}}\text{.}$
Work Step by Step
$\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\frac{6}{7}$
This is the sum of fractions where the numerator value is one less than the denominator value.
The value of $k$ varies from $1$ to $5$.
Thus, the sigma notation is,
$\sum\limits_{k=1}^{5}{\frac{k+1}{k+2}}$
Thus, the sigma notation for the sum $\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\frac{6}{7}$ is$\sum\limits_{k=1}^{5}{\frac{k+1}{k+2}}\text{.}$
