找规律计算：1/x(x+2)+1/(x+2)(x+4)+1/(x+4)(x+6)+……1/（x+2004)(x+2006)_数学解答

找规律计算：1/x(x+2)+1/(x+2)(x+4)+1/(x+4)(x+6)+……1/（x+2004)(x+2006)

人气：108 ℃　时间：2019-11-04 04:39:45

解答

1/x(x+2)+1/(x+2)(x+4)+1/(x+4)(x+6)+……1/（x+2004)(x+2006)
=1/2[1/x-1/(x+2)]+1/2[1/(x+2)-1/(x+4)]+1/2[1/(x+4)-1/(x+6)]+……+1/2[1/(x+2004)-1/(x+2006)]
=1/2[1/x-1/(x+2)+1/(x+2)-1/(x+4)+1/(x+4)-1/(x+6)+……+1/(x+2004)-1/(x+2006)]
=1/2[1/x-1/(x+2006)]
=1003/x(x+2006)