共50条信息
已知数列\(\{a_{n}\}\)的首项\(a_{1}=1\),前\(n\)项的和为\(S_{n}\),且满足\(2a_{n+1}+S_{n}=2(n∈N^{*})\),则满足\(\dfrac{1\mathrm{\ }001}{1\mathrm{\ }000} < \dfrac{S_{2n}}{S_{n}} < \dfrac{11}{10}\)的\(n\)的最大值为 \(.\)
数列\(\left\{ {{a}_{n}} \right\}\)是各项为正数的等比数列,且\({{a}_{4}}=2\),已知函数\(f(x)={\log }_{ \frac{1}{2}}x \),则\(f\left( a_{1}^{3} \right)+f\left( a_{2}^{3} \right)+\cdot \cdot \cdot +f\left( a_{7}^{3} \right)=\)( )
已知等比数列\(\{\)\(a_{n}\)\(\}\)满足\(a\)\({\,\!}_{1}=3\),\(a\)\({\,\!}_{1}+\)\(a\)\({\,\!}_{3}+\)\(a\)\({\,\!}_{5}=21\),则\(a\)\({\,\!}_{3}+\)\(a\)\({\,\!}_{5}+\)\(a\)\({\,\!}_{7}=(\) \()\)
在等比数列\(\{a_{n}\}\)中,\(S_{n}\)表示前\(n\)项和,若\(a_{3}=2S_{2}+1\),\(a_{4}=2S_{3}+1\),则公比\(q\)等于________.
\((1)\)求\(\{\)\(a_{n}\)\(\}\)的通项公式;
\((2)\)求\(\{\)\(b_{n}\)\(\}\)的前\(n\)项和.
已知首项为\(\dfrac{3}{2}\)的等比数列\(\{{{a}_{n}}\}\)的前\(n\)项和为\({{S}_{n}}\),\((n\in {{N}^{*}})\),且\(-2{{S}_{2}},{{S}_{3}},4{{S}_{4}}\)成等差数列,
\((\)Ⅰ\()\)求数列\(\{{{a}_{n}}\}\)的通项公式;
\((\)Ⅱ\()\)求\({{S}_{n}}(n\in {{N}^{*}})\)的最值.
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