(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

PROVE rigorously from the definition that

lim (3^{n})/(n!) = 0.

n->∞

2. Relevant equations

N/A

3. The attempt at a solution

By definition, a real number sequence

a(n)->a iff

for all ε>0, there exists an integer N such that n≥N => |a(n) - a|< ε.

|(3^{n})/(n!)|<...< ε

Nowhow can I find N?The usual approach to find N would be to set |a(n) -L|< ε and solve the inequality for n. But here in |(3^{n})/(n!)|<...< ε, I don't think we can solve for n. (because n is appearing everywhere. n(n-1)(n-2)...2x1, and n also appears on the numerator)

Any help is greatly appreciated!

[note: also under discussion in Math Links forum]

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# Homework Help: Prove rigorously: lim (3^n)/(n!) = 0

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