职教组卷基于海量职教高考试题库建立的在线组卷及学习系统
职教组卷
  • 题型:解答题 题类:模拟题 难易度:较易

    已知数列\(\{a _{n} \}\)满足\(a _{1} =1\),\(a _{n} = \sqrt {3}a_{n-1}+ \sqrt {3}-1(n\geqslant 2,n∈N^{*})\),\(b _{n} =a _{n} +1\).
    \((\)Ⅰ\()\)求证:数列\(\{b _{n} \}\)是等比数列;
    \((\)Ⅱ\()\)已知\(c _{n} = \dfrac {2a_{n}}{[2( \sqrt {3})^{n-1}-1](2n-1)(2n+1)}\),求数列\(\{c _{n} \}\)的前\(n\)项和\(T _{n}\).
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