3x(1x2+2x3+3x4+…+9x100)
2个回答
2014-10-02
展开全部
1+2+3+....+n=n(n+1)/2
1²+2²+3²+......+n²=n(n+1)(2n+1)/6
1x2+2x3+3x4+...+99x100
=1x1+2x2+3x3+...+99x99+(1+2+3+.....+99)
=99x100x199/6+(1+99)*99/2
=328350+4950
=333300
3X333300
=999900
1²+2²+3²+......+n²=n(n+1)(2n+1)/6
1x2+2x3+3x4+...+99x100
=1x1+2x2+3x3+...+99x99+(1+2+3+.....+99)
=99x100x199/6+(1+99)*99/2
=328350+4950
=333300
3X333300
=999900
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