### An infinite continued fraction of $x^n$

I coded in SageMath to compute the 50^{th} convergent of $f(x)$ and plot for integers $x=1,\dots,50$:

```
def f(x, n_terms):
result = []
for i in range(n_terms):
result.extend([x**i, x**i])
return continued_fraction([0] + result).n()
list_plot(([f(x,50) for x in range(1,50)]), title='$f(x)=\\dfrac{x}{x+\\dfrac{x^2}{x^2+\\dfrac{x^3}{x^3+\\ddots}}}$')
```

My question is to make a continuous plot of $f(x)$.
I have difficulty in that `continued_fraction`

only support integer values of $x$.