1/(2*4)+1/(4*6)+1/(6*8)+.+1/(2008*2010)

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1/(2*4)+1/(4*6)+1/(6*8)+.+1/(2008*2010)
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1/(2*4)+1/(4*6)+1/(6*8)+.+1/(2008*2010)
1/(2*4)+1/(4*6)+1/(6*8)+.+1/(2008*2010)

1/(2*4)+1/(4*6)+1/(6*8)+.+1/(2008*2010)
1/(2*4)+1/(4*6)+1/(6*8)+.+1/(2008*2010)
=1/2*[1/2-1/4+1/4-1/6+1/6-1/8+……+1/2008-2010]
=1/2*[1/2-1/2010]
=251/1005