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1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7

1只+1只=1双; 1(个月)+2(个月)=1季度 3天+4天=1周 5个月+7个月=1年 6(小时)+18小时=1天

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+···+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

1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+1/5*6*7+1/6*7*8+1/7*8*9+1/8*9*10+1/9*10*11 =(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)[(1/9*10)-(1/10*11)] =(1/2)[(1/1*2)-(1/2*3)+(1/2*3)-(1/3*4)+(1/3*4)-(1/4*...

原是=4/2(1/1*2-1/2*3)+5/2(1/2*3-1/3*4)+6/2(1/3*4-1/4*5)+…… +11/2(1/8*9-1/9*10) 这是第一次裂项,将(1*2*3)分之4裂成4/2(1/1*2-1/2*3) (2*3*4)分之5裂成5/2(1/2*3-1/3*4)……依次类推 继续运算得 原是=1+1/2{1/2*3+1/3*4+……+1/8*9}-(11/2...

1/n(n+1)(n+2)(n+3) =1/(n^2+3n)(n^2+3n+2) =1/2[1/(n^2+3n)-1/(n^2+3n+2)] =1/2[1/n(n+3)-1/(n+1)(n+2)] 1/1*2*3*4+1/2*3*4*5+1/3*4*5*6+-----+1/17*18*19*20 =1/2[1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5+-----+1/17*20-1/18*19] =1/2[1/1*4+1/2...

1、这是一道六年级的数奥题,要用“分数的拆分法”来解答才行。 2、就是说,把题目中的所有分数拆成两个分数相减的形式,形成加减相互抵消,从而达到不同分的目的。 3、这道题首先把题中的分数拆分成下面的样子: 1/1*2*3=[1/(1×2)-1/(2×3)]×...

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+……1/599*600 =1-1/2+1/2-1/3+1/3-1/4+……+1/599-1/600 =1-1/600 =599/600

解: 1/(1×3)+1/(2×4)+1/(3×5)+1/(4×6)+……+1/(99×101) =[1/(1×3)+1/(3×5)+…+1/(99×101)]+[1(2×4)+1/(4×6)+1/(6×10)+…+1/(96×98)] =(1-1/3+1/3-1/5+…+1/99-1/101)/2+(1/2-1/4+1/4-1/6+…+1/96-1/98)/2 =(1-101)/2+(1/2-1/98)/2 =50/101+12/49 =366...

1/((n-1)*n*(n+1))=0.5*(1/(n-1)*n-1/n*(n+1))=0.5*[(1/(n-1)-1/n)-(1/n-1/(n+1))]=0.5*(1/(n-1)+1/(n+1)-2/n) 也就是说1乘2乘3的分之一就是1加上3分之一减去2分之2,再乘以0.5后得到结果6分之一 记住这个公式哦 高三毕业都要用的哈 努力啊

=1/2[(1-1/3)+(1/2-1/4)+(1/3-1/5)+......+(1/17-1/19)+(1/18-1/20) =1/2[1+1/2-1/3+1/3-1/4+1/4-......-1/18+1/18-1/19-1/20] =1/2(1+1/2-1/19-1/20) =(1/2)*(531/380) =531/760

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