解
原式
=(1-1/2)+(1/2-1/3)+……+(1/2005-1/2006)
=1+(1/2-1/2)+(1/3-1/3)+……+(1/2005-1/2005)-1/2006
=1-1/2006
=2005/2006
裂项
1/n(n+1)=1/n-1/(n+1)