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Limit with factorial

  • Thread starter Kuno
  • Start date
  • #1
19
0

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.
 

Answers and Replies

  • #2
Curious3141
Homework Helper
2,843
87
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.
 
  • #3
540
2
Forget about the limit, how do you simplify:

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

(LOL, Curious3141 is faster than me)
 
  • #4
Curious3141
Homework Helper
2,843
87
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:
 
  • #5
19
0
Ah yes, that makes perfect sense. Thanks.
 

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