排列\( n(n - 1)(n - 2) \cdots 3 \cdot 2 \cdot 1 \)的逆序数是（ ）
A: \( {1 \over 2}n(n - 1) \)
B: \( n(n - 1) \)
C: \( n \)
D: \( {n^2}(n - 1) \)
A: \( {1 \over 2}n(n - 1) \)
B: \( n(n - 1) \)
C: \( n \)
D: \( {n^2}(n - 1) \)
举一反三
- \( {1 \over {1 + x}} \)的麦克劳林公式为（ ）。 A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \) D: \( {1 \over {1 + x}} = 1 - x - { { {x^2}} \over 2}- \cdots - { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \)
- \( {1 \over {1 + x}} \)的麦克劳林公式为（ ）. A: \( {1 \over {1 + x}} = 1 + x + { { {x^2}} \over 2} + \cdots + { { {x^n}} \over {n!}} + o\left( { { x^n}} \right) \) B: \( {1 \over {1 + x}} = 1 + x + {x^2} + \cdots + {x^n} + o\left( { { x^n}} \right) \) C: \( {1 \over {1 + x}} = 1 - x + {x^2} - \cdots + {( - 1)^n}{x^n} + o\left( { { x^n}} \right) \)
- 1．下列数列中，收敛但极限不为$1$的是 A: ${{(2+\frac{1}{n})}^{\frac{1}{n}}}$ B: ${{n}^{\frac{1}{n}}}$ C: $\frac{1}{{{n}^{2}}+1}+\frac{2}{{{n}^{2}}+2}+\cdots +\frac{n}{{{n}^{2}}+n}$ D: $\frac{{{(n!)}^{2}}}{{{n}^{n}}}$
- 设`\n`阶方阵`\A`满足`\|A| = 2`，则`\|A^TA| = ,|A^{ - 1}| = ,| A^ ** | = ,| (A^ ** )^ ** | = ,|(A^ ** )^{ - 1} + A| = ,| A^{ - 1}(A^ ** + A^{ - 1})A| = `分别等于（ ） A: \[4,\frac{1}{2},{2^{n - 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^n},\frac{{{3^n}}}{2}\] B: \[2,\frac{1}{2},{2^{n - 1}},{2^{{{(n + 1)}^2}}},2{(\frac{3}{2})^n},\frac{{{3^n}}}{2}\] C: \[4,\frac{1}{2},{2^{n + 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^{n - 1}},\frac{{{3^n}}}{2}\] D: \[2,\frac{1}{2},{2^{n - 1}},{2^{{{(n - 1)}^2}}},2{(\frac{3}{2})^{n - 1}},\frac{{{3^n}}}{2}\]
- 下列级数中,收敛的是（ ）. A: \(<br/>\sum\limits_{n = 1}^\infty { { 1 \over n}} \) B: \(<br/>\sum\limits_{n = 1}^\infty { { 1 \over { { n^2}}}} \) C: \(<br/>\sum\limits_{n = 1}^\infty { { 1 \over {\sqrt n }}} \) D: \( \sum\limits_{n = 1}^\infty { { 1 \over {\root 3 \of { { n^2}} }}} \)