Limit of a sequence

Calculus Level 5

Let us define $k_0=0$ and $k_{n+1}=k_n+\sqrt{1+k_n^2}$ .

Find the value of $\lim_{n \rightarrow \infty} \left(\dfrac{k_n}{2^n}\right)$

Also try Limit of a sequence (2) and (3)

$\textbf{Assumptions and Source}$

$n$ is any non-negative integer.
This is a standard problem in most calculus textbooks for $\text{JEE (Advanced)}$ .