共50条信息
数列\(\{a_{n}\}\)满足\(a_{1}=1\),且\(a_{n+1}=a_{1}+a_{n}+n(n∈N^{*})\),则\( \dfrac{1}{a_{1}}+ \dfrac{1}{a_{2}}+…+ \dfrac{1}{a_{2 016}}\)等于\((\) \()\)
当\(n\geqslant 2\)时,\( \dfrac{1}{n^{2}-1}= \dfrac{1}{2}\left( \left. \dfrac{1}{n-1}- \dfrac{1}{n+1} \right. \right).(\) \()\)
\({{a}_{n}}=2{{n}^{2}}-n\),以下四个数是数列\(\left\{ {{a}_{n}} \right\}\)中的一项的是( )
数列\(-1,\dfrac{4}{3},-\dfrac{9}{5},\dfrac{16}{7},\cdots \)的一个通项公式是\((\) \()\)
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\(\{a_{n}\}\)是首项为\(1\),公差为\(2\)的等差数列,数列\(\{b_{n}\}\)满足\(\dfrac{{{a}_{{1}}}}{{{b}_{{1}}}}+\dfrac{{{a}_{{2}}}}{{{b}_{{2}}}}+\dfrac{{{a}_{{3}}}}{{{b}_{{3}}}}+\ldots +\dfrac{{{a}_{n}}}{{{b}_{n}}}=\dfrac{{1}}{{{{2}}^{n}}}\),若数列\(\{b_{n}\}\)的前\(n\)项和为\(S_{n}\),则\(S_{5}=\)
在数列\(\{{{a}_{n}}\}\)中,\({{a}_{\ 1}}=2,{{a}_{n+1}}={{a}_{n}}+\ln (1+\dfrac{1}{n})\),则\({{a}_{n}}=\) \((\) \()\)
已知\(f\left(n\right)= \dfrac{1}{n+1}+ \dfrac{1}{n+2}+ \dfrac{1}{n+3}+...+ \dfrac{1}{2n}\left(n∈{N}^{*}\right), \)那么\(f\left(n+1\right)-f\left(n\right) \)等于 \((\) \()\)
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