Tính  \(B = \dfrac{2}{{3.5}} + \dfrac{3}{{5.8}} + \dfrac{{11}}{{8.19}} + \dfrac{{13}}{{19.32}} + ... + \dfrac{{25}}{{32.

* Hướng dẫn giải

Ta có:

\(\begin{array}{l}B = \dfrac{2}{{3.5}} + \dfrac{3}{{5.8}} + \dfrac{{11}}{{8.19}} + \dfrac{{13}}{{19.32}} + ... + \dfrac{{25}}{{32.57}} + \dfrac{{30}}{{57.87}}\\B = \left( {\dfrac{{5 - 3}}{{3.5}}} \right) + \left( {\dfrac{{8 - 5}}{{5.8}}} \right) + -. + \left( {\dfrac{{87 - 57}}{{57.87}}} \right)\\B = \left( {\dfrac{1}{3} - \dfrac{1}{5}} \right) + \left( {\dfrac{1}{5} - \dfrac{1}{8}} \right) + -. + \left( {\dfrac{1}{{57}} - \dfrac{1}{{87}}} \right)\\B = \dfrac{1}{3} - \dfrac{1}{{87}} = \dfrac{{28}}{{87}}\end{array}\)