Sandwich rule for sequences I'm taking a first year calculus course and I'm stuck on a concept with sequences. The question asks to use the sandwich rule to find the following limits of sequences:
 (1)
and
 (2)
I've shown that (1) = 3 by factoring out 3^n to 3(1)^1/n, and that (2) = 0 as n! = n(n-1)(n-2)... and n^n = n.n.n... which is clearly larger. However, I have no idea how to apply the sandwich rule here. The way we've been taught is to use a simple case and build it up:

Can anyone give me a few examples on how to approach these types of questions, or other resources to turn to?

hint: $3 < (3^n+1)^{1/n} < 3\cdot 2^{1/n}$, and $0 < \dfrac{n!}{n^n} < \dfrac{1}{n}$
