WBJEE · Maths · Limits
The value of \(\lim _{n \rightarrow \infty} \frac{(n !)^{n}}{\frac{1}{n}}\) is
- A 1
- B \(\frac{1}{e^{2}}\)
- C \(\frac{1}{2 e} \quad\)
- D \(\frac{1}{e}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{e}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \infty} \frac{(n !)^{1 / n}}{n}=\lim _{n \rightarrow-}\left(\frac{n !}{n^{n}}\right)^{1 / n}\) We have, \(\frac{n !}{n^{n}}=\frac{1 \cdot 2 \cdot 3}{n \cdot n \cdot n} \frac{n}{n}\)…
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