共50条信息
已知数列\(\left\{ {{a}_{n}} \right\}\)满足\({{a}_{1}}=2,{ }{{a}_{n+1}}=1-\dfrac{1}{{{a}_{n}}}\),则\({{a}_{2018}}=(\) \()\)
已知数列\(\left\{ {{a}_{n}} \right\}\)满足:\({{a}_{1}}=1\),\({{a}_{n+1}}=\dfrac{{{a}_{n}}}{{{a}_{n}}+2}\) \(\left( n\in {{N}^{*}} \right).\)若\({{b}_{n+1}}=\left( n-2\lambda \right)\cdot \left( \dfrac{1}{{{a}_{n}}}+1 \right)\) \(\left( n\in {{N}^{*}} \right)\),\({{b}_{1}}=-\lambda \),且数列\(\left\{ {{b}_{n}} \right\}\)是单调递增数列,则实数\(\lambda \)的取值范围是____。
已知数列\(\{{{a}_{n}}\}\)中,\({{a}_{1}}=1\),\({{a}_{n+1}}=c+\dfrac{1}{{{a}_{n}}}\),且\(1\leqslant {{a}_{n}}\leqslant 4\),则\(c\)的取值范围是___\(.\)
已知数列\(\left\{ {{a}_{n}} \right\}\)满足:\({{a}_{1}}=3\),\({{a}_{n+1}}=\dfrac{1}{1-{{a}_{n}}}\),则\({{a}_{2020}}=(\) \()\)
设\(f(n)=1+\dfrac{1}{2}+\dfrac{1}{3}+\cdots +\dfrac{1}{2n+1}(n\in {{N}^{*}})\),则\(n=1\)时,\(f(n)=\)( )
己知数列\(\{a_{n}\}\)满足\({{a}_{n}}=\begin{cases} & (1-3a)n+10a,n\leqslant 6 \\ & {{a}^{n-7}},n < 6 \end{cases}(n∈N^{+})\),若\(\{a_{n}\}\)是递减数列,则实数\(a\)的取值范围是\((\) \()\)
已知数列\(\{a_{n}\}\)满足\({{a}_{n+1}}=\dfrac{1}{1-{{a}_{n}}}(n∈N*)\),\(a_{8}=2\),则\(a_{1}\)的值为\((\) \()\)
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