1/2x4+1/4x6+1/6x8+...+1/2006x2008

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1/2x4+1/4x6+1/6x8+...+1/2006x20081/2x4+1/4x6+1/6x8+...+1/2006x20081/2x4+1/4x6+1/6x8+...+1/2006x20081

1/2x4+1/4x6+1/6x8+...+1/2006x2008
1/2x4+1/4x6+1/6x8+...+1/2006x2008

1/2x4+1/4x6+1/6x8+...+1/2006x2008
1/2X4+1/4X6+1/6X8+...+1/2006X2008=1/2(1/2-1/4+1/4-1/8+1/8-1/16+...+1/2006-2008)
=1/2(1/2-1/2008)=1003/(1004*4)