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材料;1x2=1/3x(1x2x3%0x1x2) 2x3=1/3x(2x3x4%1x2x...

(1)1/3*(1*2*3-0*1*2+2*3*4-1*2*3+...+10*11*12-9*10*11)=440 (2)1/3*n*(n+1)*(n+2) (3)1/4*(1*2*3*4-0*1*2*3+2*3*4*5-1*2*3*4+...+7*8*9*10-6*7*8*9)=1260

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

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

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)/2 1x2x3+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

(1)(n-1)n(n+1)-n³ =(n²-1)n-n³ =n³-n-n³ =-n; 所以(n-1)n(n+1)-n³=-n (2)带入第一问,当n=1000时 999*1000*1001=-1000

(1)1/3(100x101x102) (2)1/3(n x (n+1) x (n+2)) (3)1/4(n x (n+1) x(n+2) x(n+3))

162/54

解:因为1x2x3=(1x2x3×4-0x1x2×3)/4 2x3x4=(2x3x4×5-1x2x3×4)/4 ......... 7x8x9=(7x8x9×10-6x7x8x9)/4 所以 1x2x3+2x3x4+3x4x5+…+7x8x9 =(1x2x3×4-0x1x2×3)/4+(2x3x4×5-1x2x3×4)/4+...(7x8x9×10-6x7x8x9)/4 =(7x8x9×10)/4 =1260

x1是x下角一个1吗?

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