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

    已知等比数列\(\{a_{n}\}\)的公比为\(q(q≠1)\),前\(n\)项和为\(S_{n}\),\(S_{3}=14\),且\(3a_{2}\)是\(2a_{3}\)与\(4a_{1}\)的等差中项.
    \((1)\)求\(\{a_{n}\}\)的通项公式;
    \((2)\)设\(b_{n}=\dfrac{1}{(\log_{2}a_{n+1})(\log_{2}a_{n+2})}\),\(\{b_{n}\}\)的前\(n\)项和为\(T_{n}\),证明:\(T_{n}< \dfrac {1}{2}.\)
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