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1ʮ2x2ʮ3x3ʮ ʮnxn

0.

n(n+1)(2n+1)/6

һ1^2+2^2+3^2++n^2=n(n+1)(2n+1)/6 l*l+2*2++n*n=n*(n+1)*(2*n+1)61^3+2^3+3^3+4^3+5^3+6^3+n^3=n^2*(n+1)^2/4 1^3+2^3+3^3+4^3+5^3+6^3+n^3=(1+2+3+.+n)^2ġ1*2+2*3+3*4+4*5+5*6+6*7++n(n+1)=n(n+1)(n+2)/3 塢1+2+3+4+5+6+7+8+9++n=n(n+1)/2 1+3+5+7+9+11+13+15++(2n-1)=n^2 ߡ2+4+6+8+10+12+14++(2n)=n(n+1)

1x2ʮ2x3ʮ3x4ʮʮ10x11 =1^2+1+2^2+2+3^2+3++10^2+10 =(1^2+2^2+3^2++10^2)+(1+2+3++10) =10*(10+1)*(2*10+1)/6+10*(10+1)/2 =10*11*12/3 =440 ,׷,ףѧϰ!

=(n+1)!-1

1x1һ2x2ʮ3x3һ4x4ʮ5x5ʮ99x99һ100x100=(1+2)(1-2)+)3+4)(3-4)++(99+100)(99-100)=-(1+2+3+4++99+100)=-(1+100)x1002=-5050

: 1/1x2ʮ1/2x3ʮ1/3x4ʮʮ1/98x99ʮ1/99x100 =1-1/2+1/2-1/3+1/3-1/4++1/98-1/99+1/99-1/100 =1-1/100 =99/100

3xһ4x^2ʮ7-3x+2x^2ʮ1= -2x^2ʮ8x=-3ԭʽ =-2x^2ʮ8=-2*9+8=-10

1X2+2X3+3X4+4X5++99X100 ֱü㹫ʽ1/3*(N-1)N(N+1) :1x2ʮ2x3ʮʮ99x100=1/3*99*100*101=333300

1*2=1*3(1*2*3-0*1*2)2*3=1/3(2*3*4-1*2*3).10*11=1/3(10*11*12-9*10*11)1x2+2x3+3x4++10x11=1/3(10*11*12-0*1*2)=440

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