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

[Kuno]

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.

 

[Curious3141]

Forget about the limit and just focus on simplifying algebraically. You know that $${(n+1)}! = n!{(n+1)}$$. Also $$3^{n+1} = (3)(3^n)$$. Use those to cancel some terms and see what you get.

 

[yenchin]

Forget about the limit, how do you simplify:

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

(LOL, Curious3141 is faster than me)

 

[Curious3141]

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!

 

[Kuno]

Ah yes, that makes perfect sense. Thanks.