已知|ab-2|与|a-1|互为相反数,求下列式子的值1/ab+1/(a+1)(b+1)+...+1/(a+2006)(b+20060超急要写出计算过程及思路

Question

已知|ab-2|与|a-1|互为相反数,求下列式子的值
1/ab+1/(a+1)(b+1)+...+1/(a+2006)(b+20060
超急
要写出计算过程及思路

Answer 1

因为|ab-2|≥0|a-1|≥0且|ab-2|与|a-1|互为相反数所以|ab-2|=|a-1|=0所以a=1,b=2.所以1/ab+1/(a+1)(b+1)+...+1/(a+2006)(b+2006）=1/2+1/2*3+...+1/2007*2008=1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008=1-1/2008=2007/...