|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=?
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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=?](/uploads/image/z/444762-18-2.jpg?t=%EF%BD%9C1%2F2001-1%2F2000%EF%BD%9C%2B%EF%BD%9C1%2F2000-1%2F1999%EF%BD%9C-%EF%BD%9C1%2F1999-1%2F2001%EF%BD%9C%3D%3F1%2F2%2B1%2F4%2B1%2F8%2B...%2B1%2F256%2B1%2F512%2B1%2F1024%3D%3F1%2B2%2B3%2B...%2B1997%2B1998%2B1999%3D%3F)
|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=?
|1/2001-1/2000|+|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=?
|1/2001-1/2000|+|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
(1)原式=1/2000-1/2001+1/1999-1/2000-(1/1999-1/2001)
=1/2000-1/2001+1/1999-1/2000-1/1999+1/2001
=0
(2)原式=(1-1/2)+(1/2-1/4)+(1/4-1/8)……+(1/512-1/1024)
=1-1/1024
=1023/1024
(3)原式=(1+1999)*1999/2=1999000
|1/2001-1/2000|+|1/2000-1/1999|-|1/1999-1/2001|=0
1\2+1\4+1\8+...+1\256+1\512+1\1024
=1\2+1\4+1\8+...+1\256+1\512+1\1024+1\1024-1\1024
=1-1/1024
=1023/1024
1+2+3+...+1997+1998+1999
=(1+1999)+(2+1998)+(3+1997)+...+(999+1001)+1000
=1998000+1000
=1999000
(3)(1+1999)+(2+1998)+(3+1997)+...+(999+1001)+1000=2001000