1x2+2x3......+100x101

如题所述

第1个回答 2010-10-14

1x2+2x3+3x4+4x5+...+99x100+100x101
=2(1+3)+4(3+5)+6(5+7)+...+98(97+99)+100(99+101)
=2*4+4*8+6*12+...+98*196+100*200
=2*2²+2*4²+2*6²+...+2*100²
=2(2²+4²+6²+...+100²)
=本回答被提问者采纳

第2个回答 2010-10-14

1*2+2*3+3*4+…+n(n+1)+…+100*101
=(1^2+1)+(2^2+2)+(3^2+3)+…+(n^2+n)+…+(100^2+100)
=(1^2+2^2+3^2)+…n^2+…+100^2)+(1+2+3+…+n+…+100)
=[n(n+1)(2n+1)/6]+[n(1+n)/2] (n=100 带入）
=n(n+1)(n+2)/3
=343400

n^2 为 n的平方

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