Doubts in showing following $\lim_{n\to \infty}p^{1/n}=1$

Question

$\lim_{n\to \infty}p^{1/n}=1$

I can able to show this limit for $p\geq 1$ but I came across problem for $0<p<1$
As I had choose $a_n$ as $a_n =1-p^{1/n}>0$ Now $p^{1/n}=1-a_n$ So $(1-a_n)^n=p$
I wanted to use binomial but I could not able to proceed due to negative sign.
Any Help will be appreciated

Answer 1

If $0<p<1$ then $(\frac 1 p)^{1/n} \to 1$ because $\frac 1 p>1$. Hence $\frac 1 {p^{1/n}} \to 1$ so $p^{1/n} \to 1$.

Answer 2

Let $q=\frac1p>1$ then

$$p^\frac1n =\frac1{q^\frac1n} \to 1$$