time complexity - Homework: Prove or disprove: (5n)!=O(n!^5) -

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i have question in h.w:

prove or disprove: (5n)!=o(n!^5).

i don't know how approach (of course know o notation definition don't have clue how solve it).. please?

i think have use stirling's approximation here, gives following approximations:

since known that:

we have:

if need more detailed proof, can indeed use big o formal definition, still stirling's approximation, obtain result.


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