Question

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...1/(x+2005)(x+2006)

Answer 1

有等式1/(x+1)(x+2)=1/(x+1)-1/(x+2)

所以左边=1/(x+1)-1/（x+2）+1/(x+2)-1/(x+3).

=1/(x+1)-1/(x+2006)

后面就不用我说了吧 左右移一下统分就可以了