2/x(x+2)+2/(x+2)(x+4)+...+2/(x+2004)(x+2006)

问题描述:

2/x(x+2)+2/(x+2)(x+4)+...+2/(x+2004)(x+2006)

1/x - 1/(x+2006)
2/x(x+2)=1/x - 1/(x+2)
所以原式=1/x -1/(x+2) +1/(x+2)+.+1/(x+2004) -1/(x+2006)