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1x2ʮ2x3ʮ3x4ʮ 99x100

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

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

1X2ʮ2X3ʮ3X4ʮ4X5ʮʮ98X99ʮ99X100 =2X(1+3)+4X(3+5)+6X(5+7)++98X(97+99)+99X100 =8X(1X1+2X2+3X3+4X4+5X5+6X6+7X7++49X49)+99X100 =8X1/6X49X(49+1)X(2X49+1)+99X100 =8X1/6X49X50X99+99X100 =323400+9900 =333300

õӷ ͼ: ѧеĻ,Ҳƽ͹ʽֱӼ

1-1/2+1/2-1/3+1/3..+1/99-1/100=1-1/100=99/100

ԭʽ=3*(1-1/2+1/2-1/3+1/3-1/4++1/99-1/100)=3*99/100=297/100.

O(_)O;3x(99x100x101-0x1x2)]=99x100x101=999900 ʲô׿׷,ⲻ,½,лл.ʮ99x100)=3x[1/,½ǡΪش ɱ,ⷢҵͷ..:3x(1x2+2x3ʮ3x4+

: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

1x2+2x3+3x4+4x5..99x100=1/3*1*2*3+1/3*[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]++1/3[99*100*101-98*99*100]=1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+.+99*100*101-98*99*100]=1/3*99*100*101=3300*101=333300

1x1+2x2+3x3+4x4++100x100-(1+2+3+4+..100)=100x(100+1)x(2x100+1)/6-(1+100)x100/2=100x101x201/6-101x100/2=338350-5050=333300

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