question_answer

Let \[a={{3}^{\frac{1}{223}}}+1,\] for all \[n\ge 3\] and let \[f(x)={}^{n}{{C}_{0}}{{a}^{n-1}}-{}^{n}{{C}_{1}}{{a}^{n-3}}+{}^{n}{{C}_{2}}{{a}^{n-3}}-.....+{{(-1)}^{n-1}}{}^{n}{{C}_{n-1}}{{a}^{0}}.\] If the value of \[f\left( 2007 \right)+f\left( 2008 \right)\text{ }=\text{ }{{3}^{k}},\] where \[k\in N,\] then the value of k is ____.

A)  3                                

B)  6

C)  9

D)  12

E)  None of these