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

题目

｜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=?

答案

=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=1999...