\(\frac{5}{2}+\frac{5}{6}+\frac{5}{12}+...+\frac{5}{110}=5\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)
\(=5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=5\left(1-\frac{1}{11}\right)=5.\frac{10}{11}=\frac{50}{11}\)