请帮我回答几道奥数题,请帮我回答几道奥数题,1.1/2（二分之一）+5/6+11/12+19/20+29/30+.+9701/9702+9899/99002.(1+2/5)*(1-2/5)*(1-2/7)*.*(1+2/2005)8(1-2/2005)3.1+1/2+(1/3+2/3)+.+(1/50+2/50+3/50+...+49/50)4.(1+1/2)*(1-1/2)*.*(1+1/9

请帮我回答几道奥数题,请帮我回答几道奥数题,1.1/2（二分之一）+5/6+11/12+19/20+29/30+.+9701/9702+9899/99002.(1+2/5)*(1-2/5)*(1-2/7)*.*(1+2/2005)8(1-2/2005)3.1+1/2+(1/3+2/3)+.+(1/50+2/50+3/50+...+49/50)4.(1+1/2)*(1-1/2)*.*(1+1/9
请帮我回答几道奥数题,
请帮我回答几道奥数题,
1.
1/2（二分之一）+5/6+11/12+19/20+29/30+.+9701/9702+9899/9900
2.
(1+2/5)*(1-2/5)*(1-2/7)*.*(1+2/2005)8(1-2/2005)
3.
1+1/2+(1/3+2/3)+.+(1/50+2/50+3/50+...+49/50)
4.
(1+1/2)*(1-1/2)*.*(1+1/99)*(1-1/99)
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请帮我回答几道奥数题,请帮我回答几道奥数题,1.1/2（二分之一）+5/6+11/12+19/20+29/30+.+9701/9702+9899/99002.(1+2/5)*(1-2/5)*(1-2/7)*.*(1+2/2005)8(1-2/2005)3.1+1/2+(1/3+2/3)+.+(1/50+2/50+3/50+...+49/50)4.(1+1/2)*(1-1/2)*.*(1+1/9
1/2+5/6+11/12+19/20+29/30+.+9701/9702+9899/9900
=1-1/2+1-1/6+1-1/12+1-1/20+...+1-1/9900
=(1+1+1+...+1)-(1/2+1/6+1/12+...+1/9900)
=100-(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)
=100-(1-1/100)
=99+1/100
=9901/100
(1+2/5)*(1-2/5)*(1-2/7)*.*(1+2/2005)(1-2/2005)
=(7/5)(3/5)(9/7)(5/7)(11/9)(7/9)...(2007/2005)(2003/2005)
=(7/5*9/7*...*2007/2005)*(3/5*5/7*...*2003/2005)
=2007/5*3/2005
=6021/10025
1+1/2+(1/3+2/3)+.+(1/50+2/50+3/50+...+49/50)
=1+1/2+1+(1+1/2)+2+.+(48+1/2)
=1+1/2+2/2+3/2+4/2+.+49/2
=1+1/2*(1+2+...+49)
=1+1/2*1/2*(1+49)*49
=613.5
(1+1/2)*(1-1/2)(1+1/3)*(1-1/3)*.(1+1/99)*(1-1/99)
=3/2*1/2*4/3*2/3*...*100/99*98/99
=1/2*(3/2*2/3)*(4/3*3/4)*...*(99/98*98/99)*100/99
=1/2*100/99
=50/99

1 1/2
5/6=1-1/6=1-(1/2-1/3)=1-1/2+1/3
11/12=1-1/12=1-(1/3-1/4)=1-1/3+1/4
……
9899/9900=1-1/9900=1-(1/99-1/100)=1-1/99+1/100
原式＝1/2+1-1/2+1/3+1-1/3+1/4+……+1-1/99+1/100=99+1/100

简单

1.
1/2+5/6+11/12+19/20+29/30+.......+9701/9702+9899/9900
=（1-1/2)+(1-1/6)+(1-1/12)+……+(1-1/9900)
=99-[1/2+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)]
=99-(1-1/100)
=98又1/100
2.
(...

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1.
1/2+5/6+11/12+19/20+29/30+.......+9701/9702+9899/9900
=（1-1/2)+(1-1/6)+(1-1/12)+……+(1-1/9900)
=99-[1/2+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)]
=99-(1-1/100)
=98又1/100
2.
(1+2/5)*(1-2/5)*(1+2/7)*......*(1+2/2005)8(1-2/2005)
=7/5×3/5×5/7×……×2007/2005×2003/2005
=3/5×2007/2005
=6021/10025
3.
1+1/2+(1/3+2/3)+......+(1/50+2/50+3/50+...+49/50)
=1+1/2+1+(1+1/2)+2+(2+1/2)+......+(24+1/2)
=613.5
4.
(1+1/2)*(1-1/2)*......*(1+1/99)*(1-1/99)
=3/2×1/2×……×100/99×98/99
=1/2×100/99
=50/99

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