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1*2/1+2*3/1+3*4/1+4*5/1+5*6/1怎么做,简便

1*2/1+2*3/1+3*4/1+4*5/1+5*6/1=1-2/1+2/1-3/1+3/1-4/1+4/1-5/1+5/1-6/1=1-6/1=6/5

你那个是:原式=2+6+12+20+30=70. 不简单的算法也很简单请问你是不是打错了?这是经常的题型:若原题是1*1/2+1/2 * 1/3 +……+1/5 * 1/6,则:原式=(1-1/2)+(1/2-1/3)+……+(1/5-1/6) =1-1/6 =5/6

1*2+2*3+3*4+4*5=2+6+12+20=40对吗?

1*2/1+2*3/1+3*4/1+4*5/1+5*6/1+6*7/1+7*8/1+8*9/1+9*10/1 =1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10 =1-1/10 =9/10

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

1/1*2+1/2*3+1/3*4+1/4*5.+1/99*100=1-1/2+1/2-1/3+1/3-1/4++1/99-1/100=1-1/100=99/100

1*2/1+2*3/1+3*4/1+4*5/1+2006*2007/1 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2006-1/2007=1-1/2007=2006/2007

原式 =1/(1*2)+1/(2*3)+1/(3*4)++1/(99*100) =(1-1/2)+(1/2-1/3)+(1/3-1/4)++(1/99-1/100) =1-1/2+1/2-1/3+1/3-1/4++1/99-1/100 =1-1/100=99/100

抄反了吧1/1*2+1/2*3+1/3*4+1/4*5+省略号+1/99*100=这样吧裂项1/1*2=1-1/21/2*3=1/2-1/31/99*100=1/99-1/100原式=1-1/2+1/2-1/3+1/3+1/4++1/99-1/100 =每两项抵消 =1-1/100 =99/100

=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+……+1/2*(1/20*21-1/21*22)=1/2*(1/1*2-1/21*22)=115/231

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