知|ab-2|与|b-1|互为相反数1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
问题描述：
知|ab-2|与|b-1|互为相反数1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2009)(b+2009)
答
|ab-2|+|b-1|=0|b-1|=0b=1|ab-2|=0|a-2|=0a=21/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=1/2-1/3+1/3-1/4+1/4-1/5+...+1/2010-1/2011=1/2-1/2011=2011/4022-2/4022=...