解方程1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2005)(x+2006)=1/2x+4012

1/(x+1)(x+2)+1/(x+2)(x+3)+。+1/(x+2005)(x+2006)=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+。+1/(x+2005)-1/(x+2006)=1/(x+1)-1/(x+2006)=2005/(x+1)(x+2006)即原式化为：2005/(x+1)(x+2006)=1/2（x+2006）解得x=4009