∵ab-3的绝对值与b-1绝对值互为相反数,
∴ab-3=0 b-1=0
a=3 b=1
原式=1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+1/(a+6)(b+6)...+1/(a+2010)(b+2010)
=1/2×(1-1/3+1/3-1/5+……+1/2011-1/2013)
=1/2×2012/2013
=1006/2013
∵ab-3的绝对值与b-1绝对值互为相反数,
∴ab-3=0 b-1=0
a=3 b=1
原式=1/ab+1/(a+2)(b+2)+1/(a+4)(b+4)+1/(a+6)(b+6)...+1/(a+2010)(b+2010)
=1/2×(1-1/3+1/3-1/5+……+1/2011-1/2013)
=1/2×2012/2013
=1006/2013