# Homework Help: Limit with factorial

1. May 8, 2007

### Kuno

1. The problem statement, all variables and given/known data
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)?

2. Relevant equations

3. The attempt at a solution
I have never encountered this before.

2. May 8, 2007

### 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.

3. May 8, 2007

### yenchin

Forget about the limit, how do you simplify:

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

(LOL, Curious3141 is faster than me)

4. May 8, 2007

### Curious3141

And it's weird how we worded that almost identically!

5. May 8, 2007

### Kuno

Ah yes, that makes perfect sense. Thanks.