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职教组卷
  • 题型:解答题 题类:期中考试 难易度:中档

    在等差数列\(\{a _{n} \}\)中,\(a _{1} =3\),其前\(n\)项和为\(S _{n}\),等比数列\(\{b _{n} \}\)的各项均为正数,\(b _{1} =1\),公比为\(q\),且\(b _{2} +S _{2} =12\),\(q= \dfrac {S_{2}}{b_{2}}\).
    \((1)\)求\(a _{n}\)与\(b _{n}\);
    \((2)\)设数列\(\{c _{n} \}\)满足\(c_{n}= \dfrac {1}{S_{n}}\),求\(\{c _{n} \}\)的前\(n\)项和\(T _{n}\).
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