已知（a-1)的平方+ab-2的绝对值=0,求1/ab+1/(a+1)*(b+1)+1/(a+2)*(b+2)+…+1/(a+2009)*(b+2009)+
问题描述：
已知（a-1)的平方+ab-2的绝对值=0,求1/ab+1/(a+1)*(b+1)+1/(a+2)*(b+2)+…+1/(a+2009)*(b+2009)+
1/(a+2010)*(b+2010)的值
答
由题意a-1=0,ab-2=0
则a=1,b=2
则原式=1/2+1/2*(1/3)+1/3*(1/4)+……+1/2011*(1/2012)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2011-1/2012)
=1-1/2012
=2011/2012