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1x2=1|3(1x2x3%0x1x2) 2x3=1|3(2x3x4%1x2x3) 3x4=1...

(1) ( 10x11x12-0x1x2)x1/3=440 (2) [nx(n+1)x(n+2)-0x2x1]x1/3=1/3n^3+n^2+2/3n(3) (9x10x11-0x1x2)x1/3=924 下次有问题找我,我爸妈是数学老师.

1X2+2X3+3X4+、、、、、、+nX(n+1=1/3 ( nX(n+1)x(n+2)- 0X1X2 ) 1X2=1/3(1X2X3-0X1X2) 2X3=1/3(2X3X4-1X2X3)可见1X2=1/3(1X2X3-0X1X2) 中的前面式子1X2X3同 2X3=1/3(2X3X4-1X2X3) 抵消了如此类推,得出

【1】1x2+2x3+3x4++10x11=10*11*12/3=440【2】1x2+2x3+3x4++nx[n+1]=n(n+1)(n+2)/3【3】请类比以上形式,尝试连续三个字然数的乘积的规律并计算1x2x3+2x3x4+3x4x5++7x8x9=7*8*9*10/4=1260

(1)1x2+2x3+3x4+111+10x11=三分之一x(1x2x3-0x1x2)+三分之一x(2x3x4-1x2x3)+.+三分之一x(10x11x12-9x10x11)=三分之一x(10x11x12-0x1x2)=440 (用结合率把1/3提

【1】1x2+2x3+3x4++10x11=10*11*12/3=440 【2】1x2+2x3+3x4++nx[n+1]=n(n+1)(n+2)/3 【3】请类比以上形式,尝试连续三个字然数的乘积的规律并计算1x2x3+2x3x4+3x4x5++7x8x9=7*8*9*10/4=1260

根据以上规律:3x4=1/3(3x4x5-2x3x4)nx(n+1)=1/3[nx(n+1)x(n+2)-(n-1)xnx(n+1)]1x2+2x3+3x4+、、、、、、+nx(n+1)=1/3[1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4++nx(n+1)x(n+2)-(n-1)xnx(n+1)]=1/3[nx(n+1)x(n+2)-0x1x2]=n(n+1)(n+2)/3

3*(1x2+2x3+3x4++99x100)=3*1/3*(1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+99x100x101-98x99x100)=99x100x101 选 C

(1*1+1)+(2*2+2).=(1*1+2*2+3*3+N*N)+(1+2+3+4++N)=同理,第二题乘出来:(1*1*1+2*2*2+3*3*3+n*n*n)+3(1*1+2*2+n*n)+2(1+2+3+4+..+n)=

(1)1x2+2x3+3x4++100x101=1/3*(100*101*102-99*100*101+99*100*101.-0*1*2)=1/3*102*100*101=343400(2)1x2+2x3+3x4+n(n+1)==1/3*[n*(n+1)*(n+2)-(n-1)*n*(n+1).-0*1*2]=1/3n(n+1)(n+2)(3)1x2x3+2x3x4+3x4x5++n(n+1)(n+2)=1/4[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)+(n-1)n(n+1)(n+2).-0*1*2*3)]=1/4n(n+1)(n+2)(n+3)

一般的,有:(n-1)n(n+1)=n^3-n{n^3}求和公式:Sn=[n(n+1)/2]^2{n}求和公式:Sn=n(n+1)/21x2x3+2x3x4+3x4x5+.+7x8x9=2^3-2+3^3-3++8^3-8=(2^3+3^3++8^3)-(2+3++8)=[(8*9/2)^2-1]-8*9/2+1=1260

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