计算行列式：第一行和第一列是123.......n，主对角线都是1，其余都是0 求解行列式第一行为1 2 3 4 ...n、主对角线为1第一...
\u884c\u5217\u5f0f\u7b2c\u4e00\u52171234\u2026n\u7b2c\u4e00\u884c123\u2026n\u4e3b\u5bf9\u89d2\u7ebf\u4e3a1\u5176\u4ed6\u5168\u4e3a0\u8fd9\u662f\u300a\u722a\u578b\u300b\u884c\u5217\u5f0f\uff0c\u53ef\u4ee5 r1-r2*2-r3*3-...-rn*n\uff0c\u884c\u5217\u5f0f\u6210\u300a\u4e0b\u4e09\u89d2\u300b
Dn=|1-4-9-...-n^2 0 0 .... 0|
2 1 0 .... 0
3 0 1 .... 0
............................
n 0 0 .... 1
=2-\u2211i^2 (i=1ton)
\u6700\u540e\u4e00\u5217\u52a0\u5230\u7b2c\u4e00\u5217
n+1 2 3 ... n
-1 1 1 ... 0
-1 0 1 ... 0
0 0 0 ... 1
\u5012\u6570\u7b2c\u4e8c\u5217\u52a0\u5230\u7b2c\u4e00\u5217
\u53d1\u73b0\u7b2c\u4e00\u5217\u5012\u6570\u7b2c\u4e8c\u4e2a-1\u6d88\u62100\uff0c\u7b2c\u4e00\u4e2a\u53d8\u62101+n+(n-1)
\u4ee5\u6b64\u7c7b\u63a8\uff0c\u5012\u6570\u7b2c\u4e09\u5217\u52a0\u5230\u7b2c\u4e00\u5217
\u5230\u6700\u540e
=1+2+...+n 2 3 ... n
0 1 1.....
0 0 1
\u4e0b\u4e09\u89d2\u5143\u7d20\u90fd\u662f0
\u6240\u4ee5\u884c\u5217\u5f0f\u5373\u4e3a\u5bf9\u89d2\u7ebf\u5143\u7d20\u4e58\u79ef
=(1+2+...+n)*1*1*...*1
=n(n+1)/2
最后结果2-[n(n+1)(2n+1)/6]
爪型行列式
将第2列到第n列依次乘与1/2，1/3,1/4......1/n，加到第1列，化成上三角行列式
n!(1-1/2-1/3-1/4-......-1/n)
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