1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4,…,1/n*(n+1)=1/n-1/n+1
（1）1/1*2+1/2*3+1/3*4+…+1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006
（2）1/1*2+1/2*3+1/3*4+…+1/n*(n+1)
=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=(n+1)/(n+1)-1/(n+1)
=n/(n+1)