Notice that the numerators are just the numbers \(1, 2, 3, \cdots\) and the denominators are one more than the numerators.
\(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\cdots+\frac{50}{51}=\displaystyle\sum_{n=1}^{50}\normalsize\frac{n}{n+1}\)