|a-1|+|b-2|=0 求1/a*b+1/(a+1)*(b+1)+1/(a+2)*（b+2)+.+1/(a+2007)*(b+2007)的值

|a-1|+|b-2|=0 求1/a*b+1/(a+1)*(b+1)+1/(a+2)*（b+2)+.+1/(a+2007)*(b+2007)的值
|a-1|+|b-2|=0 求1/a*b+1/(a+1)*(b+1)+1/(a+2)*（b+2)+.+1/(a+2007)*(b+2007)的值

|a-1|+|b-2|=0 求1/a*b+1/(a+1)*(b+1)+1/(a+2)*（b+2)+.+1/(a+2007)*(b+2007)的值
绝对值相加等于0,则两项全 为0,即A=1,B=2 带入原式1/a*b+1/(a+1)*(b+1)+1/(a+2)*（b+2)+.+1/(a+2007)*(b+2007) 得：1/1*2+1/2*3+1/3*4+...+1/2008*2009 裂项,得1-1/2+1/2-1/3+1/3-1/4+..+1/2008-1/2009=2008/2009