已知|ab-1|与|b-1|互为相反数,1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+...+1/(a+2004)(b+2004)=?

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已知|ab-1|与|b-1|互为相反数,1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+...+1/(a+2004)(b+2004)=?
已知|ab-1|与|b-1|互为相反数,1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+...+1/(a+2004)(b+2004)=?

已知|ab-1|与|b-1|互为相反数,1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+1/(a+3)(b+3)+...+1/(a+2004)(b+2004)=?
首先由|a-1|+|ab-2|=0 容易得到 a=1 b=2
则 1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/[(a+2004)(b+2004)]
=1/2+1/2*3+1/3*4+...+1/2003*2004
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2005-1/2006)
=1-1/2006
=2005/2006