若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)
问题描述：
若|a-1||+|ab-2|=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)
还有就是｜1/3-1/2｜+｜1/4-1/3｜+｜1/5-1/4｜+.+｜1/10-1/9｜计算
答
a=1,b=2因为1/(1*2)=1/1-1/2 1/(2*3)=1/2-1/3所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2005)(b+2005)=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2006*2007)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2006-1/2007)=1-1/2007=200...