√(a-1)+√(b-2)=0
则a=1,b=2
1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
.
1/2009*2010=1/2009-1/2010
1/ab+1/(a+2)(b+2)+.1/(a+2008)(b+2008)
=1/1*2+1/2*3+1/3*4+.+1/2009*2010
=1-1/2+1/2-1/3+1/3-1/4+.+1/2009-1/2010
=1-1/2010
=2009/2010