利用这一规律计算:2/(x+1)(x+3) + 2/(x+3)(x+5) + 2/(x+5)(x+7) + …+ 2/(x+2005)(X+2007)

问题描述:

利用这一规律计算:2/(x+1)(x+3) + 2/(x+3)(x+5) + 2/(x+5)(x+7) + …+ 2/(x+2005)(X+2007)

原式=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+1/(x+5)-1/(x+7)……+1/(x+2005)-1/(x+2007)=1/(x+1)-1/(x+2007)=
2006/(x+1)(x+2007)