\(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{2550}=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{50.51}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{50}-\frac{1}{51}=\frac{1}{3}-\frac{1}{51}=\frac{16}{51}\)
\(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{2550}=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{50\cdot51}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\)
\(=\frac{1}{3}-\frac{1}{51}=\frac{16}{51}\)
\(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{2550}\)
\(=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{50\cdot51}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{50}-\frac{1}{51}\)
\(=\frac{1}{3}-\frac{1}{51}=\frac{16}{51}\)