How does [[1 + (1/z)]^z]^(1/3) approach e^(1/3) as z approaches infinity?

[weirdobomb]

Homework Statement

Would you give me a clue as to how, limit as z approaches infinity,
[[1 + (1/z)]^z]^(1/3) = e^(1/3)

Homework Equations

The Attempt at a Solution

 

[lurflurf]

You should know that

$$\lim_{z \rightarrow \infty} \left( 1+\frac{1}{z}\right) ^z =e$$

Your result follows from it

 

[weirdobomb]

is there some sort of proof? or should i take it as it is for now?edit: nevermind, i read e on wikipedia.