解算式：2/(x+1)(x+3)+2/(x+3)(x+5)+.+2/(x+2001)(x+2003)
问题描述：
解算式：2/(x+1)(x+3)+2/(x+3)(x+5)+.+2/(x+2001)(x+2003)
加急
答
2/(x+1)(x+3)+2/(x+3)(x+5)+.+2/(x+2001)(x+2003)=[1/(x+1) -1/(x+3)]+[1/(x+3) -1/(x+5)]+.+[1/(x+2001) -1/(x+2003)]= 1/(x+1) - 1/(x+2003)= [(x+2003)-(x+1)]/[(x+1)(x+2003)]= 2002/[(x+1)(x+2003)]