[Calculus] Sequence Limits: n -> infinity (n/n^n)(Use Sandwich Rule?)

[raaznar]

Homework Statement

Use sandwich Rule to find the limit lim n> infinity (a_n) of the sequences, for which the nth term, a_n, is given.

Homework Equations

$^{lim}_{n\rightarrow∞}\frac{n!}{n^{n}}$

The Attempt at a Solution

I know by just looking at it, n^n Approaches infinity much faster than n! which results in limit approaching 0, which is the answer. But the question says to use Sandwich Rule? I don't know which 2 functions to use to bound n!/n^n between? Usually if there was a sin function, I could start with it between -1 and 1. But I don't know where to start for this question?

 

[Dick]

Homework Statement

Use sandwich Rule to find the limit lim n> infinity (a_n) of the sequences, for which the nth term, a_n, is given.

Homework Equations

$^{lim}_{n\rightarrow∞}\frac{n!}{n^{n}}$

The Attempt at a Solution

I know by just looking at it, n^n Approaches infinity much faster than n! which results in limit approaching 0, which is the answer. But the question says to use Sandwich Rule? I don't know which 2 functions to use to bound n!/n^n between? Usually if there was a sin function, I could start with it between -1 and 1. But I don't know where to start for this question?

Expand it. n!/n^n=(n/n)*((n-1)/n)*((n-2)/n)*...*(3/n)*(2/n)*(1/n). Does that give you any ideas?