Hi. I was wondering if someone could show me how to prove this statement,

let P > 0, prove that (P^(1/n) is a monotone sequence and deduce by using a subsequence that the limit must be 1.

I understand that if 0 < P < 1, then the sequence is increasing and if P > 1, the sequence is decreasing, but how do you show it? Also, how I do use the subsequence to prove its limit?

Thanks for your help.