Đáp án đúng: D
Phương pháp giải:
Áp dụng: \(\dfrac{{n - k}}{{n.k}} = \dfrac{n}{{n.k}} - \dfrac{k}{{n.k}}\)\( = \dfrac{1}{k} - \dfrac{1}{n}\,\,\)\(\left( {k,n \in \mathbb{N};\,\,k < n} \right)\)Giải chi tiết:\(\begin{array}{l}M = \dfrac{{{3^2}}}{{2.5}} + \dfrac{{{3^2}}}{{5.8}} + \dfrac{{{3^2}}}{{8.11}} + \ldots + \dfrac{{{3^2}}}{{98.101}}\\\,\,\,\,\,\,\, = 3.\left( {\dfrac{3}{{2.5}} + \dfrac{3}{{5.8}} + \dfrac{3}{{8.11}} + \ldots + \dfrac{3}{{98.101}}} \right)\\\,\,\,\,\,\,\, = 3.\left( {\dfrac{1}{2} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{8} + \dfrac{1}{8} - \dfrac{1}{{11}} + \ldots + \dfrac{1}{{98}} - \dfrac{1}{{101}}} \right)\\\,\,\,\,\,\,\, = 3.\left( {\dfrac{1}{2} - \dfrac{1}{{101}}} \right)\\\,\,\,\,\,\,\, = 3 \cdot \dfrac{{99}}{{202}}\\\,\,\,\,\,\,\, = \dfrac{{297}}{{202}}\end{array}\)
Vậy \(M = \dfrac{{297}}{{202}}\).
Chọn D.