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1ʮ2x2ʮ3x3ʮ ʮnxn

0.

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

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!

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

1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101=1^2-2^2+3^2-4^2+5^2-6^2.-100^2+101^2=(1-2)(1+2)+(3-4)(3+4)+.(99-100)(99+100)+101^2=-(1+2+3+4.+99+100)+101^2=-101*50+101^2=101*(101-50)=5151

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

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

Ӧùʽ1+2+3+.+n=1/2*n(n+1)1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)1x2ʮ2x3ʮ3x4ʮʮ100x101=1x(1+1)ʮ2x(2+1)ʮ3x(3+1)ʮʮ100x(100+1)=(1^2+2^2+3^2+.+100*2)+(1+2+3++100)=1/6*100*101*201+1/2*101*100=1/6*10100(201+3)=10100*34=343400

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