Limit of a sequence (2)

Calculus Level 5

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

Where t1=1t_1=1 and tn=n(1+tn1)t_n=n (1+t_{n-1})

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

Assumptions and Source\textbf{Assumptions and Source}

  • nN{1}n \in \mathbb{N}-\{1\}

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

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