作业帮请帮我回答几道奥数题,
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/18 15:35:03
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)
24小时内回答谢谢
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)
24小时内回答谢谢
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+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