-3/（1*2）+5/（2*3）-7/（3*4）+9/（4*5）-…+2005/（1002*1003）
=-(1+2)/(1*2)+(2+3)/(2*3)-(3+4)/（3*4）+(4+5)/（4*5）-…-(1001+1002)/(1001*1002)+(1002+10003)/（1002*1003）
=-(1/2+1)+(1/3+1/2)-(1/4+1/3)+(1/5+1/4)+.-(1/1002+1/1001)+(1/1003+1/1002)
=-1/2-1+1/3+1/2-1/4-1/3+1/5+1/4+...-1/1002-1/1001+1/1003+1/1002
=-1+1/1002(中间两项,两两相消,只留下两项-1,1/1002)
=-1001/1002