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1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1

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*...

从8个分数的特点可以写出 (n+3)/n*(n+1)*(n+2)=x/n*(n+1)-y/(n+1)*(n+2), 对右边通分 [x(n+2)-ny]=n*(n+1)*(n+2)=(n+3)/n*(n+1)*(n+2) 两边的分子相等 (x-y)n+2x=n+3 两边的同类项系数对应相等x-y=1, 2x=3, 解得x=3/2, y=1/2 原式=1/2{[3/1*2-1/...

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

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/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...

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...

=(5*7*4*9+5*7*8*3+5*7*2*9+7*8*9+5*7*4*3+5*8*9+5*7*9+5*7*8+7*4*9)/5*7*8*9 ={5*7*(36+24+18+12+9+8)+7*9*(8+4)+5*8*9}/5*7*8*9 =(35*107+63*12+40*9)/5*7*8*9 =3745+756+360/2520 =4861/2520 =(1260+840+630+504+420+360+315+280+252)/5*7*8*...

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/6-1/7) =1-1/7 =6/7欢迎快来加入快乐学习团队哟!团队地址为: http://wenwen.soso.com/z/TeamHome.e?sp=59080

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