1/(1*2)+1/(2*3)+1/(3*4)+... ...+1/(99*100)

1/(1*2)+1/(2*3)+1/(3*4)+... ...+1/(99*100)
1/(1*2)+1/(2*3)+1/(3*4)+... ...+1/(99*100)

1/(1*2)+1/(2*3)+1/(3*4)+... ...+1/(99*100)
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

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

原式=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=99/100;
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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+1/99-1/100=1-1/100=99/100
利用公式 1/n(n+1)=1/n-1/(n+1) （理解过程：求1/n-1/(n+1)，通分， 1/n-1/(n+1)=[(n+1)-n]/n(n+1)=1/n(n+1)