Ta có : \(\frac{7}{10.11}+\frac{7}{11.12}+...+\frac{7}{69.70}=7\left(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{69.70}\right)\)
\(=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)=7\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{6}{70}=\frac{3}{5}\)