Question

一道小学奥数题,请高手帮忙!!!急

Answer 1

（1-1/2+1/3-1/4+…+1/1997-1/1998+1/1999）
/[1/（1+1999）+1/(2+2000)+1/(3+2001)+1/(4+2002)+…+1/(999+2997)+1/(1000+2998)]
=(1+1/2+1/3+1/4+…+1/1998+1/1999)-(1/2+1/4+1/6+…+1/1996+1/1998)×2
/[1/2000+1/2002+1/2004+1/2006+…+1/2996+1/2998]
=(1+1/2+1/3+1/4+…+1/1998+1/1999)-(1+1/2+1/3+…+1/998+1/999) /[1/（1+1999）+
1/(2×1000)+1/(2×1001)+1/(2×1002)+…+1/(2×1998)+1/(2×1999)]
=(1/1000+1/1001+…+1/1998+1/1999) /[(1+1/2+1/3+1/4+…+1/1998+1/1999)×1/2]
=2

Answer 2

要用初一的知识

Answer 3

2
用mathematica做的

Answer 4

这个要用数列吧

Answer 5

先做分子
1-1/2+1/3-1/4+……+1/1997-1/1998+1/1999
=1-1/2+1/3-1/4+……+1/1997-1/1998+1/1999+
(1/2+1/4+1/6+……+1/1998)-(1/2+1/4+1/6+……+1/1998)
=1+1/2+1/3+1/4+……+1/1998+1/1999-2*(1/2+1/4+1/6+……+1/1998)
=1+1/2+1/3+1/4+……+1/1998+1/1999-(1+1/2+1/3+1/4+……+1/999)
=1/1000+1/1001+1/1002+……+1/1999
再做分母
分母=1/2000+1/2002+1/2004+……+1/3996+1/3998
=1/2*(1/1000+1/1001+1/1002+……+1/1998+1/1999)
所以分子/分母=（1/1000+1/1001+1/1002+……+1/1999）/[1/2*(1/1000+1/1001+1/1002+……+1/1998+1/1999)]
=2