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            • 1.
              已知集合\(A=\{x|x=2n-1,n∈N*\}\),\(B=\{x|x=2^{n},n∈N*\}.\)将\(A∪B\)的所有元素从小到大依次排列构成一个数列\(\{a_{n}\}\),记\(S_{n}\)为数列\(\{a_{n}\}\)的前\(n\)项和,则使得\(S_{n} > 12a_{n+1}\)成立的\(n\)的最小值为 ______ .
            • 2.
              等比数列\(\{a_{n}\}\)中,\(a_{1}=1\),\(a_{5}=4a_{3}\).
              \((1)\)求\(\{a_{n}\}\)的通项公式;
              \((2)\)记\(S_{n}\)为\(\{a_{n}\}\)的前\(n\)项和\(.\)若\(S_{m}=63\),求\(m\).
            • 3.
              已知等比数列\(\{{{a}_{n}}\}\)满足\({{a}_{1}}=\dfrac{1}{4}\),\(a_{3}a_{5} =4({{a}_{4}}-1)\),则\(a_{2} =\)
              A.\(2\)
              B.\(1\)
              C.\(\dfrac{1}{2}\)

              D.\(\dfrac{1}{8}\)
            • 4.

              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\(\lambda \)

            • 5.
              等比数列\(\{ \)\(a_{n}\)\(\}\)满足 \(a\)\({\,\!}_{1}= 3\), \(a\)\({\,\!}_{1}+\) \(a\)\({\,\!}_{3} +\) \(a\)\({\,\!}_{5} = 21\),则 \(a\)\({\,\!}_{3}+\) \(a\)\({\,\!}_{5} +\) \(a\)\({\,\!}_{7} =(\)    \()\)
              A.\(21\)                  
              B.\(42\)                  
              C.\(63\)                  
              D.\(84\)
            • 6.

              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。

            • 7. 已知数列{log2(an-1)}(n∈N*)为等差数列,且a1=3,a3=9.
              (Ⅰ)求数列{an}的通项公式;
              (Ⅱ)证明++…+<1.
            • 8.
              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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