Question

Thực hiện pháp tính : \(\dfrac{4}{5}+\dfrac{-3}{5.8}+\dfrac{-11}{8.19}+\dfrac{-12}{19.31}+\dfrac{-70}{31.101}+\dfrac{-99}{101.200}\)

Answer 1

\(=\dfrac{4}{1\cdot5}-\left(\dfrac{3}{5\cdot8}+\dfrac{11}{8\cdot19}+\dfrac{12}{19\cdot31}+\dfrac{70}{31\cdot101}+\dfrac{99}{101\cdot200}\right)\)

\(=1-\dfrac{1}{5}-\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{101}+\dfrac{1}{101}-\dfrac{1}{200}\right)\)

\(=1-\dfrac{1}{5}-\dfrac{1}{5}+\dfrac{1}{200}\)

\(=\dfrac{201}{200}-\dfrac{2}{5}=\dfrac{201-80}{200}=\dfrac{121}{200}\)