1/2*1/3+1/3*1/4+1?

Answer 1

小学5年级奥数题。1/2*1/3+1/3*1/4+1/4*1/5+1/6*1/7+1/7*1/8+1/8*1/9

对任意的整数n都有(1/n)*[1/(n+1)]=1/n-1/(n+1)
1/2*1/3+1/3*1/4+1/4*1/5+1/6*1/7+1/7*1/8+1/8*1/9
=1/2-1/3+1/3-1/4+……+1/8-1/9
=1/2-1/9
=7/18

1/1+1/2-1=1/2,1/3+1/4-1/2=1/12,1/5+1/6-1/3=1/30,1/7+1/8-1/4=1/56,......找规律

1/（2n-1）+1/(2n)-1/n=1/[(2n-1)x2n] 1006

七年级数学问题1/3+1/3*1/5+1/5*1/7+1/7*1/9+........1/99*1/101=?

原式=（1-1/3+1/3-1/5+1/5-1/7+……+1/99-1/101）÷2
=（1-1/101）÷2
=100/101 ÷2
=50/101

1/2=1/3+1/6;1/3=1/4+1/12;1/4=1/5+1/201/n=1/a+1/b,a+b=

1/n=1/a+1/b,a=n+1，b=n(n+1)，a+b=n+1+n(n+1)=(n+1)的平方

1/2×1/3+1/3×1/4+1/4×1/5+……+1/9×1/10

1/2×1/3 = 1/(2×3) = (3-2)/(2×3) = 3/(2×3) -2/(2×3) = 1/2 - 1/3
同样，1/3×1/4 = 1/3 - 1/4，后面的也这样变形
最后相加后只剩下 1/2 - 1/10 = 2/5

计算1/2*5+1/5*8+1/8*11+...+1/98*101 、 1/1*2*3+1/2*3*4+1/3*4*5+...+1/8*9*10

1/2*5+1/5*8+1/8*11+...+1/98*101
＝1/3×（1/2-1/5+1/5-1/8+1/8-1/11+......1/98-1/101）
＝1/3×（1/2-1/101）
＝1/3×99/202
＝33/202

五年级上奥数题1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)

1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(9*11)
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)
=1/2(1-1/3+1/3-1/5+...+1/9-1/11)
=1/2(1-1/11)
=5/11

八年级数学题：2/3=1/2+1/6 2/5=1/3+1/15 2/7=1/4+1/28 2/9=1/5+1/45

一般结论是：
2/(2n-1)=1/n+1/n(2n-1);(n>=2)
说明
计算下就好了
1/n+1/n(2n-1)=[(2n-1)+1]/n*(2n-1)=2/(2n-1);
验证
n=2;
2/(2n-1)=2/3
1/n+1/n(2n-1)=1/2+1/2*3=1/2+1/6;
n=3
2/(2n-1)=2/5
1/n+1/n(2n-1)=1/3+1/3*5=1/3+1/15
....

1/3+|/6=1/2 1/5+1/20=1/4 1/4+1/12=1/3 1/（ ）十1/（）=

1/6+1/30=1/5
1/10+1/90=1/9