高中数学选择性必修 第二册（381题）

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知识点：第四章 数列

参考答案：解：设数列\(\left\{ {{b_n}} \right\}\)的前\(n\)项和为\({T_n}\)，
\(\because {b_m} + {b_{m + 1}} + {b_{m + 2}} = \frac{1}{{{a_m}}} = \frac{m}{5}\)，
\(\therefore {T_{30}} = \left( {{b_1} + {b_2} + {b_3}} \right) + \left( {{b_4} + {b_5} + {b_6}} \right) + \cdots + \left( {{b_{28}} + {b_{29}} + {b_{30}}} \right)
= \frac{1}{5} + \frac{4}{5} + \cdots + \frac{{28}}{5}
= \frac{{10 \times \left( {\frac{1}{5} + \frac{{28}}{5}} \right)}}{2}\)\( = 29\).