(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/05 18:05:21
![(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]](/uploads/image/z/245107-19-7.jpg?t=%EF%BC%881-1%2F2%2B1%2F3-1%2F4.%2B1%2F1997-1%2F1998%2B1%2F1999%29%2F%5B1%2F%281%2B1999%29%2B1%2F%282%2B2000%29%2B1%2F%283%2B2001%29.%2B1%2F%28999%2B2997%29%2B1%2F%281000%2B2998%29%5D)
(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]
(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]
(1-1/2+1/3-1/4.+1/1997-1/1998+1/1999)/[1/(1+1999)+1/(2+2000)+1/(3+2001).+1/(999+2997)+1/(1000+2998)]
分子=1+1/2+1/3+...+1/1999 - 2*(1/2+1/4+...+1/1998)
=1+1/2+1/3+...+1/1999 - 1-1/2-1/3+...-1/999
=1/1000+1/1001+...+1/1999
分母=1/2000+1/2002+...+1/3998
=(1/1000+1/1001+...+1/1999)/2
所以原分数等于2
分子=1+1/2+1/3+...+1/1999 - 2*(1/2+1/4+...+1/1998)
=1+1/2+1/3+...+1/1999 - 1-1/2-1/3+...-1/999
=1/1000+1/1001+...+1/1999
分母=1/2000+1/2002+...+1/3998
=(1/1000+1/1001+...+1/1999)/2
分子=1+1/2+1/3+...+1/1999 - 2*(1/2+1/4+...+1/1998)
=1+1/2+1/3+...+1/1999 - 1-1/2-1/3+...-1/999
=1/1000+1/1001+...+1/1999
分母=1/2000+1/2002+...+1/3998
=(1/1000+1/1001+...+1/1999)/2
故原分数等于2