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=(1/2)/(3/2)+(1/3)/(3/2*4/3)+(1/4)/(3/2*4/3*5/4)+...+(1/99)/(3/2*4/3*...*100/99)
=(1/2)/(3/2)+(1/3)/(4/2)+(1/4)/(5/2)+...+(1/99)/(100/2)
=2/2*3+2/3*4+2/4*5+...+2/99*100
=2*(1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100)
=2*(1/2-1/100)
=49/50
=(1/2)/(3/2)+(1/3)/(4/2)+(1/4)/(5/2)+...+(1/99)/(100/2)
=2/2*3+2/3*4+2/4*5+...+2/99*100
=2*(1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100)
=2*(1/2-1/100)
=49/50
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解：原式=(1/2)/(3/2)+(1/3)/(3/2*4/3)+(1/4)/(3/2*4/3*5/4)+......+(1/99)/(3/2*4/3*...*100/99)
=(1/2)/(3/2)+(1/3)/(4/2)+(1/4)/(5/2)+......+(1/99)/(100/2)
即=1/3+1/6+1/10......1/4950
即=2/(2*3)+2/(3*4)+......+2/(99*100)
=2*[1/(2*3)+1/(3*4)+......+1/(99*100)]
=2*(1/2-1/3+1/3-1/4......-1/99+1/99-1/100)
=2*(1/2-1/100)
=49/50
=(1/2)/(3/2)+(1/3)/(4/2)+(1/4)/(5/2)+......+(1/99)/(100/2)
即=1/3+1/6+1/10......1/4950
即=2/(2*3)+2/(3*4)+......+2/(99*100)
=2*[1/(2*3)+1/(3*4)+......+1/(99*100)]
=2*(1/2-1/3+1/3-1/4......-1/99+1/99-1/100)
=2*(1/2-1/100)
=49/50
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