1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!

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1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!1/1X2+1/

1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!
1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!

1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果!
1/[n(n+1)]=1/n - 1/(n+1)
原式=1/1 - 1/2 + 1/2 - 1/3 +…+1/99 - 1/100
=1- 1/100
=0.99

1/1X2+1/2x3+1/3x4+1/4x5+......+1/98x99+1/99x100=
1-1/2+1/2-1/3+1/3-1/4.....+1/99-1/100
=1-1/100
=99/100

1/1X2+1/2x3+1/3x4+1/4x5+......+1/98x99+1/99x100=
1-1/2+1/2-1/3+1/3-1/4.....+1/99-1/100
=1-1/100
=99/100

易证1/[n(n+1)]=1/n - 1/(n+1)
所以 原式=1/1 - 1/2 + 1/2 - 1/3 +…+1/99 - 1/100
=1- 1/100
=0.99

1/n(n+1)=1/n -1/(n+1),则原式=1-1/2+1/2-1/3+......+1/98-1/99+1/99-1/100=1-1/100=99/100

1/1乘2等于1/1减1/2 同理2乘3分之一等于2分之一减去3分之一 上式等于1/1-1/2+1/2--1/3+1/3......-1/99+1/99-1/100等于99/100