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:历年真题 难易度:较易

    设\(\{a_{n}\}\)是首项为\(1\)的等比数列,数列\(\{b_{n}\}\)满足\(b_{n}=\dfrac{na_{n}}{3}\),已知\(a_{1}\),\(3a_{2}\),\(9a_{3}\)成等差数列.
    \((1)\)求\(\{a_{n}\}\)和\(\{b_{n}\}\)的通项公式;
    \((2)\)记\(S_{n}\)和\(T_{n}\)分别为\(\{a_{n}\}\)和\(\{b_{n}\}\)的前\(n\)项和\(.\)证明:\(T_{n}< \dfrac {S_{n}}{2}.\)
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