因为|a-1|>=0,|b-2|>=0
所以要使|a-1|+|b-2|=0
必须有a-1=0,b-2=0
求得,a=1,b=2
1/1×2+1/2×3+1/3×4+...+1/2007×2008
=(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
因为|a-1|>=0,|b-2|>=0
所以要使|a-1|+|b-2|=0
必须有a-1=0,b-2=0
求得,a=1,b=2
1/1×2+1/2×3+1/3×4+...+1/2007×2008
=(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