15. Power Series

Find the power series representation centered at $x=0$ of the following function. Give the interval of convergence for the resulting series. 

$f\(\left\)(x\(\right\))=\(\frac{1}{1-x^3}\)$

Find the Taylor Series of $f\(\left\)(x\(\right\))=\(\cos\) x$ centered $x=\(\pi\)$. Then, write the power series using summation notation.

Find the interval of convergence for the Taylor series for $f\(\left\)(x\(\right\))=\(\sin\) x$ centered at $x=\(\frac{\pi}{2}\)$.

Find the interval of convergence for the Maclaurin series for $f\(\left\)(x\(\right\))=\(\tan\)^{-1}x$