Find a formula for the nth term of the Taylor series of f(x), centered at c
\[f(x)=\frac{1}{x}; c=1\]
\[f'(x)=\frac{-1}{x^2}\] \[f''(x)=\frac{2}{x^3}\] \[f'''(x)=\frac{-6}{x^4}\] \[f^{(4)}(x)=\frac{24}{x^5}\]
Now we can solve for f^n
\[f^{(n)}(x) = (-1)^{(n+1)}\frac{1}{x^n}\] \[f^{(n)}(c) = (-1)^{(n+1)}\]