Question

初中数学题急需帮助 谢谢!!!我很着急...请善良的您能做几道做几道!!!我一万分的感谢!!!

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+......+1/(x+2003)(x+2004)+1/(x+2004)(x+2005)

我写的可能有点乱
请您写在纸上就好了
("/"指"分数线")

Answer 1

1/x(x+1)=1/x -1/(x+1)
1/(x+1)(x+2)=1/(x+1) - 1/(x+2)
.
.
.
1/(x+2004)(x+2005) =1/(x+2004) - 1/(x+2005)

所以
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+......+1/(x+2003)(x+2004)+1/(x+2004)(x+2005)＝
1/x - 1/(x+2005)=1/x(x+2005)=

Answer 2

可化简为：1/x-1/(x+2005)

解释： 1/(x+n)(x+n+1)=1/(x+n)-1/(x+n+1)
中间的项化成这样后，可以和前后相消