# Functions, Can you solve this?

Algebra Level 5

$\large f(m+1) = (-1)^{m+1} m - 2f(m)$

Let function $$f$$, true for integers $$m$$, satisfy the above equation and $$f(1) = f(2009)$$. If $$\displaystyle \sum_{k=1}^{2008} f(k) = \Phi$$, find $$3 \Phi$$.

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