Let f be a polynomial function such that log_2(f(x))=( log_2(2+2/3+2/9+… … ∞)) · log_3(1+(f(x))/(f(1 / x))), x>0 and f(6)=37. Then Σ_n =1^10 f( n )…

Let $\displaystyle f$ be a polynomial function such that $\displaystyle \log _2(f(x))=\left(\log _2\left(2+\frac{2}{3}+\frac{2}{9}+\ldots \ldots \infty\right)\right) \cdot \log _3\left(1+\frac{f(x)}{f(1 / x)}\right), x>0$ and $\displaystyle f(6)=37$. Then $\displaystyle \sum_{\mathrm{n}=1}^{10} f(\mathrm{n})$ is equal to $\displaystyle \_\_\_\_$.