The question is
$f_n(x) = ax^n + b \cos(x/n)$ is a sequence of functions where $f_n: [0,1] \to \mathbb{R}$. Determine for which $a,b \in \mathbb{R}$ values, $f_n$ is Cauchy w.r.t. the sup-norm in $C[0,1]$.
Since all $a,b,x$ and $n$ are variables, I can not imagine how the graph would be like for different values. I know I should show sufficient effort but in these type of questions I usually use graph of the function thus I really do not know where to start.
Can you give me some hints?
Thank you in advance.