## Calculus: Early Transcendentals 8th Edition

$\sum_{i=1}^{19}\frac{i}{i+1}$
We contract the sum into sigma notation by noting that it follows the pattern of a sum of fractions with integers 1-19 on top and a denominator increased by 1 (e.g. $\frac{i}{i+1}$): $\displaystyle \frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\cdots+\frac{19}{20}=\sum_{i=1}^{19}\frac{i}{i+1}$