Ⅰmn-2Ⅰ+Ⅰm-1Ⅰ=0,求1/mn+1/(m+1)(n+1)+1/(m+2)(n+2)+.+1/(m+2003)(n+2003)=?急.
问题描述：
Ⅰmn-2Ⅰ+Ⅰm-1Ⅰ=0,求1/mn+1/(m+1)(n+1)+1/(m+2)(n+2)+.+1/(m+2003)(n+2003)=?急.
答
简单``````听我道来`````：首先 由|mn-2|+|m-1|=0 可以知道：mn=2 且m=1从而算出m=1 , n=21/mn+1/(m+1)(n+1)+1/(m+2)(n+2)+.+1/(m+2003)(n+2003)也就等于：1/1*2 + 1/2*3 + 1/3*4 + 1/4*5……+1/2004*2005...