Limit of 3^n/n! as n approaches infinity

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We find the limit of 3^n/n! as n approaches infinity. The result is given without proof and intuition is used. We use the fact that n! grows faster than 3^n for n sufficiently large. This is true in general that factorials grows faster than exponentials. I hope this helps someone who is learning about limits and studying calculus.

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No. Not enough. n! is greater than 3^n because n! ≈ some c·n^n (ref. Stirling's formula) and n^n is obviously growing faster than 3^n at some point where n > 3.

rursus

We find these videos helpful. Keep up the good work.

sophiaisabelle

Why don’t you use the Ratio Test to solve it?

SebaCorrea

Would it be valid to bring up the fact that the series that uses this sequence sums to e^3?

yamsang__

Lim n tends to infinity {3n+7ni/2n+5i} solution please....

mohammedsiddiq

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