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ehrenfest
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[SOLVED] proving a seqeunce converges
Prove that the sequence [itex]\frac{n!}{n^n}[/itex] converges to 0.
Given [itex]\epsilon > 0[/itex], how do I find N? We know that the nth term is less than or equal to
[tex]\left(\frac{n-1}{n}\right)^{n-1}[/tex]
but that really does not help.
Homework Statement
Prove that the sequence [itex]\frac{n!}{n^n}[/itex] converges to 0.
Homework Equations
The Attempt at a Solution
Given [itex]\epsilon > 0[/itex], how do I find N? We know that the nth term is less than or equal to
[tex]\left(\frac{n-1}{n}\right)^{n-1}[/tex]
but that really does not help.