Ta có \(S=\frac{2016}{5}+\frac{2016}{10}+\frac{2016}{30}+...+\frac{2016}{47530}+\frac{2016}{48150}\)
\(=\frac{2016}{5}.\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9506}+\frac{1}{9630}\right)\)
\(=\frac{2016}{5}.\left(\frac{1}{1}+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{97.98}+\frac{1}{98.99}\right)\)
\(=\frac{2016}{5}.\left(\frac{1}{1}+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\right)\)
\(=\frac{2016}{5}.\left(1+1-\frac{1}{99}\right)\)
\(=\frac{2016}{5}.\frac{197}{99}\)
\(=\frac{44128}{55}\)
