Let $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be infinitely differentiable and suppose that

$\displaystyle f(\frac{1}{n})= \frac{n^{2}}{n^{2}+1}$for all $\displaystyle n=1,2,3,...$. Determine the values of$\displaystyle f^{'}(0), f^{''}(0), f^{'''}(0), f^{(4)}(0),...$.