2001/2002+2003/2004+2005/2006+2007/2008+2009/2010=1-1/2002+1-1/2004+1-1/2006+1-1/2008+1-1/2010=5-（1/2002+1/2004+1/2006+1/2008+1/2010）设a=2006即原式=5-{1/（a-4）+1/（a-2）+1/a+1/（a+2）+1/（a+4）}=5-{1/（a-4）+1/（a+4）+1/（a-2）+1/（a+2）+1/a}