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|1/2001-1/2000|+|1/2000-1/1999|-|1/1999-1/2001|=?

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|1/2001-1/2000|+|1/2000-1/1999|-|1/1999-1/2001|=?
1/2+1/4+1/8+...+1/256+1/512+1/1024=?
1+2+3+...+1997+1998+1999=?
=1/2000-1/2001+1/1999-1/2000+1/2001-1/1999
=0
=1/2+1/4+1/8+...+1/256+1/512+1/1024+1/1024-1/1024
=1/2+1/4+1/8+...+1/256+1/512+1/512-1/1024
=...
=1-1/1024
=1023/1024
=(1+1999)*1999/2
=2000/2*1999
=1000*1999
=1999000