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  • 题型:解答题 题类:月考试卷 难易度:较难

    设等差数列\(\{a _{n} \}\)的前\(n\)项和为\(S _{n}\),且\(5S _{5} =S _{10}\),\(a _{4} =2a _{6} +20\).
    \((1)\)求数列\(\{a _{n} \}\)的通项公式;
    \((2)\)若数列\(\{b _{n} \}\)满足\( \dfrac {b_{1}}{a_{1}} + \dfrac {b_{2}}{a_{2}} +…+ \dfrac {b_{n}}{a_{n}} = \dfrac {1}{2^{n}} -1\),\(n∈N*\),证明:\(b _{n} \leqslant \dfrac {5}{8}\).
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