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

1/2*4+1/4*6+1/6*8+....+1/2008*2010
=1/2*1/4+1/4*1/6+1/6*1/8+....+1/2008*1/2010
=1/2-1/4+1/4-1/6+1/6-1/8+....+1/2008-1/2010
=1/2-1/2010
=1004/2010
=502/1005