Question

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

Answer 1

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