What is the Taylor Series for $f(x)=(x-1)^3$ centered at $x=0$? What is the radius of convergence?
\begin{align}f'(x)&= (3)(x-1)^2\\ f''(x)&=6(x-1)\\ f^{(3)}(x)&=6\\ f^{(4)}(x)&=0\\ &\vdots\end{align}
Using the definition of Taylor Series, not sure how to put together the Taylor Series if the above is correct...
Hint:
After correcting the first derivative ( as suggested in the comments), use exactly the formula of the series with $a=0$.
Since the forth derivative is null only the first four terms of the series are not null.