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  • 题型:解答题 题类:模拟题 难易度:中档

    已知数列\(\{a _{n} \}\)中,\(a _{1} =1\),\(a_{n+1}= \dfrac {(n+1)a_{n}}{n+2a_{n}}(n∈N^{*})\).
    \((1)\)求证:\(\{ \dfrac {n}{a_{n}}\}\)是等差数列;
    \((2)\)若\(c _{n} =a _{n} a _{n+1}\),且数列\(b_{n}= \dfrac {4}{3^{n}\cdot n}\),数列\(\{b _{n} c _{n} \}\)的前\(n\)项和为\(T _{n}\),求\(T _{n}\)的取值范围.
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