1/x(x+1)+1/(x+)(x+2)+.1/(x+2005)(x+2006)
=1/x-1/(x+1)+1/(x+1)-1/(x+1)+...+1/(x+2005)-1/(x+2006)
=1-1/(x+2006)
=(x+2005)/(x+2006)
当x=1时
原式=2006/2007