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
1/1x2 + 1/2x3 + 1/3x4 + ....+ 1/2004x2005 + 1/2005x2006
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 + .....+ 1/2005 - 1/2006
= 1 - 1/2006
= 2005/2006