- #1

frasifrasi

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converges to zero (by squeeze theorem)??

Thank you! : )

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- Thread starter frasifrasi
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- #1

frasifrasi

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converges to zero (by squeeze theorem)??

Thank you! : )

- #2

dynamicsolo

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converges to zero (by squeeze theorem)??

Thank you! : )

If the Squeeze Theorem is required as part of the proof, how about comparing

[tex]\frac{4^{n}}{n!}[/tex] < [tex]\frac{4^{n}}{n^{n}}[/tex] (for n > 1)

and showing that the latter goes to zero as n--> infinity?

- #3

Gib Z

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- #4

learningphysics

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as n->infinity n^n>n! so [tex]\frac{4^n}{n!} > \frac{4^{n}}{n^{n}}[/tex].

I think probably the idea being expressed was to use a constant in the denominator instead of n. [tex]\frac{4^n}{8^n}[/tex]. (or any constant^n in the denominator where the constant>4)

[tex]\frac{4^n}{n!}< \frac{4^n}{8^n}[/tex] for large enough n.

I think probably the idea being expressed was to use a constant in the denominator instead of n. [tex]\frac{4^n}{8^n}[/tex]. (or any constant^n in the denominator where the constant>4)

[tex]\frac{4^n}{n!}< \frac{4^n}{8^n}[/tex] for large enough n.

Last edited:

- #5

dynamicsolo

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Whoops! Quite so -- I was only looking at the denominators. That needs to be n > 2 , doesn't it? (n=3 works...)

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