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Dangerous Limit

Calculus Level 3

\[ \Large \displaystyle \xi(k) = \lim_{x\rightarrow \infty} \left( \dfrac{ (k x)!}{x^{kx}} \right)^{1/x} , \quad k \in \mathbb N\]

Choose the correct option.

\\[\\xi(2) = \\dfrac{4}{e}\\] None of these \\[\\xi(2) = \\dfrac{1}{e}\\] \\[\\xi(1) = \\dfrac{2}{e}\\] \\[\\xi(1) = \\dfrac{1}{e}\]

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by Akhil Bansal

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