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  • 题型:解答题 题类:单元测试 难易度:中档

    年份:2020

    已知\(\{a _{n} \}\)是等差数列,其前\(n\)项和为\(S _{n}\),\(\{b _{n} \}\)是正项递增的等比数列,且\(a _{1} =b _{1} =2\),\(a _{3} =b _{3}\),\(S _{5} -b _{5} =8\).
    \((1)\)求数列\(\{a _{n} \}\)与\(\{b _{n} \}\)的通项公式;
    \((2)\)记\(T _{n} =a _{n} b _{1} +a _{n-1} b _{2} +…+a _{1} b _{n}\),\(n∈N ^{*}\),求\(T _{n}\).
  • 题型:解答题 题类:单元测试 难易度:中档

    年份:2020

    已知首项都是\(1\)的数列\(\{a _{n} \}\),\(\{b _{n} \}(b _{n} \neq 0 , n∈N ^{*} )\)满足\(a _{n} b _{n+1} -a _{n+1} b _{n} +2b _{n} b _{n+1} =0\)
    \((I)\)令\(c _{n} = \dfrac {a_{n}}{b_{n}}\),求数列\(\{c _{n} \}\)的通项公式;
    \((\)Ⅱ\()\)令数列\(b _{n} =3 ^{n+1}\),求数列\(\{a _{n} \}\)的前\(n\)项和\(S _{n}\).