Relationship between sequence limit ($N \rightarrow R$) and corresponding function limit ($R \rightarrow R$)

Question

I have the sequence ($N \rightarrow R$):

$$ n \, \left( 2^{1/n} \, - \, 1 \right) $$

If I consider the limit:

$$ \lim_{n \rightarrow + \infty} {n \, \left( 2^{1/n} \, - \, 1 \right)} $$

and the limit of the function ($R \rightarrow R$):

$$ \lim_{x \rightarrow + \infty} {x \, \left( 2^{1/x} \, - \, 1 \right)} $$

is there some formal mathematical reason that ensures me that the two limits are equal?

Thank you in advance.