Find the value of \[\displaystyle\prod_{k=1}^{\infty} \left(1+\dfrac{1}{t_k}\right)\]

Where \(t_1=1\) and \(t_n=n (1+t_{n-1})\)

Also try limit as a sequence (1) and (3)

\(\textbf{Assumptions and Source}\)

\(n \in \mathbb{N}-\{1\}\)

This too is a standard problem in most calculus textbooks for \(\text{JEE (Advanced)}\).

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