1/2×4+1/4×6+……+1/2008×2010

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1/2×4+1/4×6+……+1/2008×20101/2×4+1/4×6+……+1/2008×20101/2×4+1/4×6+……+1/2008×20101/2×4+1/4×6+……+1/2008×

1/2×4+1/4×6+……+1/2008×2010
1/2×4+1/4×6+……+1/2008×2010

1/2×4+1/4×6+……+1/2008×2010
1/2×4+1/4×6+……+1/2008×2010
=1/2(1/1×2+1/2×3+……+1/1004×1005)
=1/2(1-1/2+1/2-1/3+...+1/1004-1/1005)
=1/2×(1-1/1005)
=1/2×1004/1005
=502/1005