已知(a-1)²+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2009)(b+2009)+1/(a+2010)(b+2010)
问题描述：
已知(a-1)²+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2009)(b+2009)+1/(a+2010)(b+2010)
答
(a-1)²+|ab-2|=0,则a=1,b=2
所以原式=1/2+1/2*3+1/3*4+……+1/2010*2011+1/2011*2012
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2010-1/2011+1/2011-1/2012
=1-1/2012
=2011/2012