1x2+2x3+3x4+…+10x11=?1x2=1/3(1x2x3-0x1x2)2x3=1/3(2x3x4-1x2x3)3x4=1/3(3x4x5-2x3x4)1x2+2x3+3x4=1/3x3x4x5=201x2+2x3+3x4+…+n(n+1)=?《2010汕头中考》1x2x3+2x3x4+3x4x5+....+7x8x9=?
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![1x2+2x3+3x4+…+10x11=?1x2=1/3(1x2x3-0x1x2)2x3=1/3(2x3x4-1x2x3)3x4=1/3(3x4x5-2x3x4)1x2+2x3+3x4=1/3x3x4x5=201x2+2x3+3x4+…+n(n+1)=?《2010汕头中考》1x2x3+2x3x4+3x4x5+....+7x8x9=?](/uploads/image/z/763568-8-8.jpg?t=1x2%2B2x3%2B3x4%2B%E2%80%A6%2B10x11%3D%3F1x2%3D1%2F3%281x2x3-0x1x2%292x3%3D1%2F3%282x3x4-1x2x3%293x4%3D1%2F3%283x4x5-2x3x4%291x2%2B2x3%2B3x4%3D1%2F3x3x4x5%3D201x2%2B2x3%2B3x4%2B%E2%80%A6%2Bn%28n%2B1%29%3D%3F%E3%80%8A2010%E6%B1%95%E5%A4%B4%E4%B8%AD%E8%80%83%E3%80%8B1x2x3%2B2x3x4%2B3x4x5%2B....%2B7x8x9%3D%3F)
1x2+2x3+3x4+…+10x11=?1x2=1/3(1x2x3-0x1x2)2x3=1/3(2x3x4-1x2x3)3x4=1/3(3x4x5-2x3x4)1x2+2x3+3x4=1/3x3x4x5=201x2+2x3+3x4+…+n(n+1)=?《2010汕头中考》1x2x3+2x3x4+3x4x5+....+7x8x9=?
1x2+2x3+3x4+…+10x11=?
1x2=1/3(1x2x3-0x1x2)
2x3=1/3(2x3x4-1x2x3)
3x4=1/3(3x4x5-2x3x4)
1x2+2x3+3x4=1/3x3x4x5=20
1x2+2x3+3x4+…+n(n+1)=?《2010汕头中考》
1x2x3+2x3x4+3x4x5+....+7x8x9=?
1x2+2x3+3x4+…+10x11=?1x2=1/3(1x2x3-0x1x2)2x3=1/3(2x3x4-1x2x3)3x4=1/3(3x4x5-2x3x4)1x2+2x3+3x4=1/3x3x4x5=201x2+2x3+3x4+…+n(n+1)=?《2010汕头中考》1x2x3+2x3x4+3x4x5+....+7x8x9=?
1x2+2x3+3x4+…+n(n+1)
=1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1)
=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)[(2n+1)+3]/6
1x2+2x3+3x4+…+10x11
=10x(10+1)x[(10x2+1)+3]/6
=110x4
=440
用机算器吧
108505100
1x2+2x3+3x4+…+n(n+1)
=1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1)
=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)[(2n+1)+3]/6
1x2+2x3+3x4+…+10x11
=10x(10+1)x[(10x2+1)+3]/6
=110x4
=440