Question

4/8.9+4/9.10+...+4/70.71

Answer 1

\(=4\left(\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}+...+\dfrac{1}{70\cdot71}\right)\\ =4\left(\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+...+\dfrac{1}{70}-\dfrac{1}{71}\right)\\ =4\left(\dfrac{1}{8}-\dfrac{1}{71}\right)=4\cdot\dfrac{63}{568}=\dfrac{63}{142}\)