Let a=3^(1/(223))+1 and for all tgeq3, l...

Let `a=3^(1/(223))+1` and for all `tgeq3`, let ``
`f(n)=^n C_0dota^(n-1)-^n C_1dota^(n-2)+^n C_2dota^(n-3)-+(-1)^(n-1)dot^n C_(n-1)dota^0` . If the value of `f(2007)+f(2008)=3^k w h e r ek in N ,` then the value of `k` is.

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