When $R[t]/f(t) \cong R[[t]]/f(t)$

Question

Let $R$ be a $\mathbb{C}$-algebra and $f$ a monic polynomial in $R[t]$, then is well defined $\frac{R[t]}{(f)}$ , $ \frac{R[[t]]}{(f)}$ when are $\cong$ like rings?. It's sufficient that $f$ isn,t invertible?

Answer 1

$\mathbb C[t]/(t-1)\simeq\mathbb C$. What can you say about $t-1$ as a power series? And what this implies about the ideal $(t-1)$ in $\mathbb C[[t]]$?