TITLE: How to prove $\lim\limits_{n\to\infty} (n+1)^{1/n} = 1$
QUESTION [7 upvotes]: We know that $\lim\limits_{n\to\infty}n^{1/n} = 1$. Using this, how can we prove that $\lim\limits_{n\to\infty} (n+1)^{1/n} = 1$?
Recalling the proof of the former limit, I was able to modify it to prove the latter limit. But I was wondering if we could just use the limit we have already calculated to prove this limit which is related to it.

REPLY [10 votes]: Note $$1\le (n+1)^{1/n}\le (2n)^{1/n}=2^{1/n}n^{1/n}.$$ Now you could apply the Squeeze Theorem using your known limit.