优优班--学霸训练营 > 题目详情
  • 已知数列\(\{a_{n}\}\)中,\(a_{1}=2\),\(a_{n+1}=2- \dfrac {1}{a_{n}}\),数列\(\{b_{n}\}\)中,\(b_{n}= \dfrac {1}{a_{n}-1}\),其中\(n∈N^{*}\);
    \((1)\)求证:数列\(\{b_{n}\}\)是等差数列;
    \((2)\)若\(S_{n}\)是数列\(\{b_{n}\}\)的前\(n\)项和,求\( \dfrac {1}{S_{1}}+ \dfrac {1}{S_{2}}+…+ \dfrac {1}{S_{n}}\)的值.
    【考点】数列的递推关系
    【分析】请登陆后查看
    【解答】请登陆后查看
    难度:较易
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