1/x(x+2)+1/(x+1)(x+3)+1/(x+2)(x+4)+...+1/(x+2007)(x+2009)过程追_数学解答

1/x(x+2)+1/(x+1)(x+3)+1/(x+2)(x+4)+...+1/(x+2007)(x+2009)
过程追

人气：121 ℃　时间：2020-07-31 00:00:23

解答

1/x(x+2)=(1/x-1/(x+2))/2
1/(x+1)(x+3)=(1/(x+1)-1/(x+3))/2
以此类推
答案是：（1/x+1/(x+1)-1/(x+2007)-1/(x+2009)）/2...其他项都消掉了