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职教组卷
  • 题型:解答题 题类:期中考试 难易度:较易

    已知数列\(\{ \dfrac {n}{a_{n}-1}\}\)的前\(n\)项和为\(n\),数列\(\{b _{n} \}\)满足\(b _{1} =1\),\(b _{n+1} -b _{n} =a _{n}\),\(n∈N ^{*}\).
    \((1)\)求数列\(\{a _{n} \}\),\(\{b _{n} \}\)的通项公式;
    \((2)\)若数列\(\{c _{n} \}\)满足\(c _{n} = \dfrac {a_{2n}}{b_{n}^{2}}\),\(n∈N ^{*}\),求满足\(c _{1} +c _{2} +c _{3} +…+c _{n} \leqslant \dfrac {63}{16}\)的最大整数\(n\).
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