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 \(\text{JEE (Advanced)}\).
by
Pratik Shastri
