(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)

(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)
(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)

(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)
将 (1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)分解（去括号）为1-2/1+2/1-3/1+3/1.+1/1999-1/2000.因为减1-2/1又加2/1,所以+2/1与-2/1互相抵消,-3/1+3/1也抵消.+1/19991与-/1999互相抵消.1没得抵消1/2000也没得抵消,只好照 算.所以：
(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)
=1-2/1+2/1-3/1+3/1.+1/1999-1/2000
=1-（2/1-2/1）-（3/1-3/1）-.（1/1999-1/1999）-1/2000
=1-1/2000
=1999/2000

把括号全部打开
1-1/2+1/2-1/3+1/3………-1/1999+1/1999-1/2000
通过观察可以看出1/2 1/3 1/4…………1/1998 1/1999都约掉了
最后得1-1/2000=1999/2000
希望能帮到你

原题
=1-1/2+1/2-1/3+1/3-……-1/1999+1/1999-1/2000
=1+(1/2-1/2)+(1/3-1/3)+……+(1/1999-1/1999)-1/20000
=1+0+0+……+0-1/2000
=1-1/2000
=1999/2000

1+(1/2-1/2)+(1/3-1/3)+.......+(1/1999-1/1999)-1/2000
=1+0+0+.......-1/2000
=1999/2000
请采纳，谢谢