|1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|=?

|1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|=?
|1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|=?

|1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|=?
|1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|
=1-1/2+1/2-1/3+1/3-1/4+……1/2007-1/2008
=1-1/2008
=2007/2008
-------------
中间的所有数全部都抵消了.
绝对值里的运算都是正的,所以只管把绝对值号拿掉就可以了.

|1-1/2|+|1/2-1/3|+|1/3-1/4|+……|1/2007-1/2008|
=1-1/2+1/2-1/3+1/3-1/4+......+1/2007-1/2008
=1-1/2008
=2007/2008

=2007/2008