计算:1/n(n+1)+1/(n+1)(n+2)+.+1/(n+2004)(n+2005)

问题描述:

计算:1/n(n+1)+1/(n+1)(n+2)+.+1/(n+2004)(n+2005)

原式=[1/n-1/(n+1)]+[1/(n+1)-1/(n+2)]+……+[[1/(n+2004)-1/(n+2005)]
中间正负抵消
所以=1/n-1/(n+2005)
=2005/(n^2+2005n)