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职教组卷
  • 题型:解答题 题类:期中考试 难易度:中档

    记\(S _{n}\)是正项数列\(\{a _{n} \}\)的前\(n\)项和,\(a _{n} + \dfrac {3}{2}\)是\(6\)和\(S _{n} + \dfrac {1}{24}\)的等比中项,且\(a _{1} \neq 2\).
    \((1)\)求\(\{a _{n} \}\)的通项公式;
    \((2)\)若等比数列\(\{b _{n} \}\)的公比为\( \dfrac {1}{2}\),且\( \dfrac {1}{b_{1}}\),\( \dfrac {1}{b_{2}}\),\( \dfrac {1}{b_{3}} -2\)成等差数列,求数列\(\{a _{n} b _{n} \}\)的前\(n\)项和\(T _{n}\).
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