1*2+2*3+3*4+···+10*11求写过程、急!

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1*2+2*3+3*4+···+10*11求写过程、急!

1*2+2*3+3*4+···+10*11求写过程、急!
1*2+2*3+3*4+···+10*11求写过程、急!

1*2+2*3+3*4+···+10*11求写过程、急!
提示:1*2=1/3(1*2*3-0*1*2),2*3=1/3(2*3*4-1*2*3),3*4=1/3(3*4*5-2*3*4)以上三式相加可得1*2+2*3+3*4=1/3*3*4*5=20.
找规律,套公式.用给的提示解题.如下:
1*2+2*3+3*4+.+10*11
=1/3(1*2*3-0*1*2)+1/3(2*3*4-1*2*3)+1/3(3*4*5-2*3*4)+.+1/3(10*11*12-9*10*11)
=1/3(1*2*3-0*1*2+2*3*4-1*2*3+3*4*5-2*3*4+.+10*11*12-9*10*11)
=1/3(10*11*12-0*1*2)
=1/3*10*11*12
=440
将提示中的每一项都提出“1/3” .将括号中的项互相抵消,得出 “ =1/3(10*11*12-0*1*2) ”.然后计算

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