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 \(\text{JEE (Advanced)}\).

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