Answer
$\sum_{i=3}^{23}\frac{i}{i+4}$
Work Step by Step
We contract the sum into sigma notation by noting that it follows the pattern of a sum of fractions with integers 3-23 on top and a denominator increased by 4 (e.g. $\frac{i}{i+4}$):
$\displaystyle \frac{3}{7}+\frac{4}{8}+\frac{5}{9}+\frac{6}{10}+\cdots+\frac{23}{27}=\sum_{i=3}^{23}\frac{i}{i+4}$