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:期中考试 难易度:较易

    已知数列\(\{a _{n} \}\),\(\{b _{n} \}\)满足\(2S _{n} =(a _{n} +2)b _{n}\),其中\(S _{n}\)是数列\(\{a _{n} \}\)的前\(n\)项和.
    \((1)\)若数列\(\{a _{n} \}\)是首项为\( \dfrac {2}{3}\),公比为\( \dfrac {1}{3}\)的等比数列,求数列\(\{b _{n} \}\)的通项公式;
    \((2)\)若\(b _{n} =n\),\(a _{2} =3\).
    \((ⅰ)\)求\(\{a _{n} \}\)通项公式;
    \((ⅱ)\)求证:\( \dfrac {1}{b_{1}a_{2}}+ \dfrac {1}{b_{2}a_{4}}+…+ \dfrac {1}{b_{n}a_{2n}} < 1\).
  • 相关试卷