Limit with Factorial: Understanding 3/(n+1) Limit

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    Factorial Limit
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Homework Help Overview

The discussion revolves around evaluating the limit of a factorial expression as n approaches infinity, specifically focusing on the relationship between the terms involving factorials and powers of 3.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore algebraic simplification of the expression involving factorials and powers of 3, questioning how to manipulate the terms to clarify the limit.

Discussion Status

Some participants have provided guidance on simplifying the expression by canceling terms, indicating a productive direction in the discussion. However, there is no explicit consensus on the final outcome or resolution of the limit.

Contextual Notes

Participants are encouraged to focus on algebraic simplification rather than directly evaluating the limit, which may indicate a specific homework guideline or approach preference.

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Homework Statement


Why does the limit as n -> infinity of [3^(n+1)]/(n+1)!] * n!/(3^n) equal
the limit as n -> infinity of 3/(n+1)?

Homework Equations


The Attempt at a Solution


I have never encountered this before.
 
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Forget about the limit and just focus on simplifying algebraically. You know that [tex]{(n+1)}! = n!{(n+1)}[/tex]. Also [tex]3^{n+1} = (3)(3^n)[/tex]. Use those to cancel some terms and see what you get.
 
Forget about the limit, how do you simplify:

[3^(n+1)]/(n+1)! * [n!/(3^n)]

(LOL, Curious3141 is faster than me)
 
yenchin said:
Forget about the limit, how do you simplify:

[3^(n+1)]/(n+1)! * [n!/(3^n)]

(LOL, Curious3141 is faster than me)

And it's weird how we worded that almost identically! :eek:
 
Ah yes, that makes perfect sense. Thanks.
 

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