已知|ab-2|+|a-2|=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|ab-2|+|a-2|=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)
答
绝对值都是非负数,两个非负数的和为0,那么这两个数都是0ab-2=0a-2=0解得:a=2,b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2010*2011)=1-1/2+1/2-1/3+1/3-1/4+...+1/201...