My question is to:
1) Calculate the coefficient of $x^n$ in the Taylor expansion of $f(x)$
2) Find the radius of convergence of this series
when $f(x)=\frac{5}{1-3x}$
For the first part I recognised that it was of the form $f(x)=\frac{a}{1-r}$ so then $f(x)=\sum_{n=0}^\infty ar^n$ which then translated as $f(x)=\sum_{n=0}^\infty 5(3x)^n$, so I concluded that the coefficient of $x^n$ was $5(3^n)$.
Secondly for the ratio of convergence, I knew that $|r|\lt 1$ so $|3x|\lt 1$ therefore the ratio of convergence is $\frac{1}{3}$.
This was for an online quiz, however it was only marked as partially correct and did not give any feedback so I am not sure which is right or wrong? If anyone could shed any light on if my answers were correct of not then that would be greatly appreciated!
RE: Solved, contacted course administrator and was CAS error!