1X2+2x3+3x4+...99x100 =
展开全部
n(n+1)
=(1/3) { n(n+1)(n+2) - (n-1)n(n+1) }
1x2+2x3+3x4+...99x100
= 1x2 + (1/3) { (2x3x4 - 1x2x3) + (3x4x5 - 2x3x4) +...+(99x100x101 - 98x99x100) }
= 1x2 + (1/3) { 99x100x101 -1x2x3 }
= (1/3) 99x100x101
=333300
=(1/3) { n(n+1)(n+2) - (n-1)n(n+1) }
1x2+2x3+3x4+...99x100
= 1x2 + (1/3) { (2x3x4 - 1x2x3) + (3x4x5 - 2x3x4) +...+(99x100x101 - 98x99x100) }
= 1x2 + (1/3) { 99x100x101 -1x2x3 }
= (1/3) 99x100x101
=333300
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