|1 / 2-1 | + | 1 / 3_ Half | + | quarter_ 1 / 3 +..., 1 / 2009-1 / 2008|

|1 / 2-1 | + | 1 / 3_ Half | + | quarter_ 1 / 3 +..., 1 / 2009-1 / 2008|

|1/2 -1|+|1/3-1/2|+|1/4-1/3|+.+|1/2009-1/2008|
=1-1/2+1/2-1/3+1/3-1/4+.1/2008-1/2009
=1-1/2009
=2008/2009
The number in each absolute value is less than zero, and the time-varying sign is removed
I don't know how to keep asking^_^