1/1*2+1/2*3+1/3*4+1/4*5+.+1/2004*2005=?

1/1*2+1/2*3+1/3*4+1/4*5+.+1/2004*2005=?

原式=1-1/2+1/2-1/3+……+1/2004-1/2005
=2004/2005

1/[n*(n+1)]=1/n-1/n+1
1/1*2+1/2*3+1/3*4+1/4*5+......+1/2004*2005
=1/1-1/2+1/2+1/3+…………-1/2004+1/2004-1/2005
=1-1/2005=2004/2005