TITLE: Prove the following limit $ \lim_{n\to \infty} (3^n + 4^n)^{1/n} = 4 $
QUESTION [8 upvotes]: How do i prove the limit below? I've tried, but i got nothing.

$ \lim\limits_{n\to \infty} (3^n + 4^n)^{1/n} = 4. $

Thanks for any help.

REPLY [8 votes]: How about:
$$=\lim_{n \to \infty} 4\left(1+\frac{3^n}{4^n}\right)^{1/n} = \lim_{n \to \infty} 4\left(1+0.75^n\right)^{1/n} = 4$$