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${Lt}_{n \to \infty} {(\frac{n!}{n})}^{1 / n} is equal to$

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Correct option is B

y=limn→∞⁡n!n1/n=limn→∞⁡n!nn1nlog⁡y=limn→∞⁡1n⋅log⁡1n⋅2n⋅3n…⋅nn=limn→∞1nlog⁡1n+log⁡2n+log⁡3n+…..+log⁡nn=Ltn→∞∑r=1∞ 1nlog⁡rn=∫01 log⁡x⋅dx=(xlog⁡x−x)01logey=−1⇒y=e−1⇒y=1e

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Ltn→∞⁡n!n1/n is equal to

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${Lt}_{n \to \infty} {(\frac{n!}{n})}^{1 / n} is equal to$