1/2*1=1-1/2
1/2*1/3=1/2-1/3
....
1/2008*1/2009=1/2008-1/2009
...
1/2*1+1/2*1/3+1/3*1/4+1/4*1/5+……+1/2008*1/2009=1-1/2009=2008/2009
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/2008-1/2009)=2008/2009.
1/2*1+2/1*3/1+3/1*4/1+4/1*5/1...+2008/1*2009/1
=(1-1/2)+(2/1-3/1)+(4/1-5/1)+(5/1-6/1)+……+(2008/1-2009/1)
=1-2009/1
=2009/2008
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