1.|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2009-1/2008|=
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/2007-1/2008)+(1/2008-1/2009)
=1/2-1/2009
=2007/4018
2.求满足|ab|+|a+b|=1的所有整数对(a,b).
|ab|+|a+b|=1
a,b为整数,所以
|ab|=0,|a+b|=1
或|ab|=1,|a+b|=0
所以
满足|ab|+|a+b|=1的所有整数对(a,b)为
(1,0),(-1,0)(0,1)(0,-1)(1,-1)(-1,1)