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n阶行列式求值?1 2 3 4 ...n-1 nn 1 2 3 ...n-2 n-1n-1 n 1 2 ...n-3 n

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n阶行列式求值?
1 2 3 4 ...n-1 n
n 1 2 3 ...n-2 n-1
n-1 n 1 2 ...n-3 n-2
...
3 4 5 6 ...1 2
2 3 4 5 ...n 1
n阶行列式求值?1 2 3 4 ...n-1 nn 1 2 3 ...n-2 n-1n-1 n 1 2 ...n-3 n
这个问题有点麻烦
(数与数之间我用逗号隔开)
首先将每一列的数都家到第一列上
原式=
n(n+1)/2,2,3,4,...,n-1,n
n(n+1)/2,1,2,3,...,n-2,n-1
n(n+1)/2,n,1,2,...,n-3,n-2
.
n(n+1)/2,4,5,6,...,1,2
n(n+1)/2,3,4,5,...,n,1
第一列提出来n(n+1)/2
原式=n(n+1)/2*
1,2,3,4,...,n-1,n
1,1,2,3,...,n-2,n-1
1,n,1,2,...,n-3,n-2
.
1,4,5,6,...,1,2
1,3,4,5,...,n,1
从最后一行开始到第二行每一行都减去自己上面的一行
原式=n(n+1)/2*
1,2,3,4,...,n-1,n
0,-1,-1,-1,...,-1,-1
0,n-1,-1,-1,...,-1,-1
.
0,-1,-1,-1,...,-1,-1
0,-1,-1,-1,...,n-1,-1
从最后一列到第3列,每一列都减去自己左面一列得
原式=n(n+1)/2*
1,2,3,4,...,n-1,n
0,-1,-1,-1,...,-1,-1
0,n,0,0,...,0,0
.
0,0,0,0,...,0,0
0,0,0,0,...,n,0
按照第一列展开得
原式=n(n+1)/2*
-1,-1,-1,...,-1,-1
n,0,0,...,0,0
0,n,0,...,0,0
.
0,0,0,...,0,0
0,0,0,...,n,0
按最后一列展开得
原式=n(n+1)/2*（-1）^(1+n-1)*(-1)*
n,0,0,...,0
0,n,0,...,0
.
0,0,0,...,0
0,0,0,...,n
=(-1)^(n+1)*n(n+1)/2*n^(n-2)
证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 n阶行列式计算|1 2 3.n-1 n||2 1 3.n-1 n||2 3 1.n-1 n||.||2 3 4. 1 n 化简(n+1)(n+2)(n+3) 2^n/n*(n+1) 化简：1/(n+1)(n+2)+1/(n+2)(n+3)+1/(n+3)(n+4) (n+1)(n+2)/1 +(n+2)(n+3)/1 +(n+3)(n+4)/1 计算：n(n+1)(n+2)(n+3)+1 lim[(n+3)/(n+1))]^(n-2) 【n无穷大】 (1/(n^2 n 1 ) 2/(n^2 n 2) 3/(n^2 n 3) ……n/(n^2 n n)) 当N越于无穷大 当n为正偶数,求证n/(n-1)+n(n-2)/(n-1)(n-3)+...+n(n-2).2/(n-1)(n-3).. 1 + (n + 1) + n*(n + 1) + n*n + (n + 1) + 1 = 2n^2 + 3n + 3