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            • 1.

              已知数列\(\{a_{n}\}\)的前\(n\)项和\(S_{n}=1+a\)\({S}_{n}=1+λ{a}_{n} \),其中\(\lambda \)\(0\)

              \((I)\)证明\(\{a\)\(n\)\(\}\)是等比数列,并求其通项公式

              \((II)\)若\({S}_{5}= \dfrac{31}{32} \) ,求\(\lambda \)

            • 2.

              已知\(\left\{ {{a}_{n}} \right\}\)是公差为\(3\)的等差数列,数列\(\left\{ {{b}_{n}} \right\}\)满足\({{b}_{1}}=1,{{b}_{2}}=\dfrac{1}{3},{{a}_{n}}{{b}_{n+1}}+{{b}_{n+1}}=n{{b}_{n}}\) .

               \((1)\)求\(\left\{ {{a}_{n}} \right\}\)的通项公式;

              \((2)\)求\(\left\{ {{b}_{n}} \right\}\)的前\(n\)项和。

            • 3.
              已知\(\{a_{n}\}\)是各项均为正数的等比数列,且\(a_{1}+a_{2}=6\),\(a_{1}a_{2}=a_{3}\).
              \((1)\)求数列\(\{a_{n}\}\)通项公式;
              \((2)\{b_{n}\}\)为各项非零的等差数列,其前\(n\)项和为\(S_{n}\),已知\(S_{2n+1}=b_{n}b_{n+1}\),求数列\(\{ \dfrac {b_{n}}{a_{n}}\}\)的前\(n\)项和\(T_{n}\).
            • 4.
              已知\(\{a_{n}\}\)为等差数列,前\(n\)项和为\(S_{n}(n∈N^{+})\),\(\{b_{n}\}\)是首项为\(2\)的等比数列,且公比大于\(0\),\(b_{2}+b_{3}=12\),\(b_{3}=a_{4}-2a_{1}\),\(S_{11}=11b_{4}\).
              \((\)Ⅰ\()\)求\(\{a_{n}\}\)和\(\{b_{n}\}\)的通项公式;
              \((\)Ⅱ\()\)求数列\(\{a_{2n}b_{2n-1}\}\)的前\(n\)项和\((n∈N^{+}).\)
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