a, Ta có :
\(C=\dfrac{7}{10.11}+\dfrac{7}{11.12}+.......+\dfrac{7}{69.70}\)
\(=7\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+.........+\dfrac{1}{69.70}\right)\)
= \(7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+........+\dfrac{1}{69}-\dfrac{1}{70}\right)\)
= \(7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=7.\dfrac{6}{70}=\dfrac{3}{5}\)
b, \(E=\dfrac{3^2}{8.11}+\dfrac{3^2}{11.14}+........+\dfrac{3^2}{197.200}\)
\(=3.\left(\dfrac{3}{8.11}+\dfrac{3}{11.14}+......+\dfrac{3}{197.200}\right)\)
= \(3.\left(\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+......+\dfrac{1}{197}-\dfrac{1}{200}\right)\)
= \(3.\left(\dfrac{1}{8}-\dfrac{1}{200}\right)=3.\dfrac{24}{200}=\dfrac{9}{25}\)
