Suppose a recursive root$-$finding algorithm for computing a true real root $x_{\text{t}\text{r}\text{u}\text{e}}$ satisfies

$e_n=k{e}_{n-1}^2,n=1,2,$dots

where $k$ is a constant independent of $n,$ and $e_n=|x_n-x_{\text{t}\text{r}\text{u}\text{e}}|$ is the absolute error after the $n$th iteration.

If the initial error $e_0=|x_0-x_{\text{t}\text{r}\text{u}\text{e}}|,$ where $x_0$ denotes the initial guess, then

$k{e}_n=(k{e}_0{)}^{2^n}$

$k{e}_n=(k{e}_0{)}^{2n}$

$k{e}_n=(k{e}_0{)}^2$