1/2001*2002+1/2002*2003+1/2003*2004+1/2004*2005+1/2005=?/?

1/2001*2002+1/2002*2003+1/2003*2004+1/2004*2005+1/2005
=(1/2001-1/2002)+(1/2002-1/2003)+(1/2003-1/2004)+(1/2004-1/2005)+1/2005
=1/2001