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1/2000*2001+1/2001*2002+1/2002*2003···+1/2007*2008
=(1/2000-1/2001)+(1/2001-1/2002)+(1/2002-1/2003)+...+(1/2007-1/2008)
=1/2000-1/2001+1/2001-1/2002+1/2002-1/2003+...+1/2007-1/2008
=1/2000-1/2008
=1/502000
=(1/2000-1/2001)+(1/2001-1/2002)+(1/2002-1/2003)+...+(1/2007-1/2008)
=1/2000-1/2001+1/2001-1/2002+1/2002-1/2003+...+1/2007-1/2008
=1/2000-1/2008
=1/502000
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