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Maths-

General

Easy

Question

Let $f left parenthesis k right parenthesis equals fraction numerator k over denominator 2009 end fraction$ and $g left parenthesis k right parenthesis equals fraction numerator f to the power of 4 end exponent left parenthesis k right parenthesis over denominator left parenthesis 1 minus f left parenthesis k right parenthesis right parenthesis to the power of 4 end exponent plus left parenthesis f left parenthesis k right parenthesis right parenthesis to the power of 4 end exponent end fraction$ then the sum $stretchy sum from k equals 0 to 2009 of g left parenthesis k right parenthesis$ is equal:

2009
2008
1005
1004

The correct answer is: 1005

$f left parenthesis k right parenthesis equals fraction numerator k over denominator 2009 end fraction$
$f left parenthesis k right parenthesis plus f left parenthesis 2009 minus k right parenthesis equals 1$
$g left parenthesis k right parenthesis plus g left parenthesis 2009 minus k right parenthesis equals 1$
$rightwards double arrow stretchy sum from k equals 0 to 2009 of g left parenthesis k right parenthesis equals 1005$

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