Question

TÍNH TỔNG: 

A = \(\frac{6}{5\times8}\)+\(\frac{22}{8\times19}\)+\(\frac{24}{19\times31}\)+\(\frac{140}{31\times101}\)+\(\frac{198}{101\times200}\)

Answer 1

\(A=\frac{6}{5.8}+\frac{22}{8.19}+\frac{24}{19.31}+\frac{140}{31.101}+\frac{198}{101.200}\)

\(A=2.\left(\frac{1}{5}-\frac{1}{8}\right)+2.\left(\frac{1}{8}-\frac{1}{19}\right)+2.\left(\frac{1}{19}-\frac{1}{31}\right)+2.\left(\frac{1}{31}-\frac{1}{101}\right)+2.\left(\frac{1}{101}-\frac{1}{200}\right)\)

\(A=2.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}+\frac{1}{19}-\frac{1}{31}+\frac{1}{31}-\frac{1}{101}+\frac{1}{101}-\frac{1}{200}\right)\)

\(A=2.\left(\frac{1}{5}-\frac{1}{200}\right)\)

\(A=2.\frac{39}{200}\)

\(\Rightarrow A=\frac{39}{100}\)