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:模拟题 难易度:中档

    已知数列\(\{a _{n} \}\)满足\(a _{1} =1\),\(\{a _{n} \}\)的前\(n\)项和\(S _{n}\)满足\(S _{n+1} =2S _{n} +n+1\).
    \((1)\)求数列\(\{a _{n} \}\)的通项公式;
    \((2)\)记数列\(\{ \dfrac {1}{a_{n}}\}\)的前\(n\)项和为\(T _{n}\),证明:\(T_{n} < \dfrac {5}{3}\).
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