Finding $\lim_{n\to\infty}\sqrt[n]{3^n + 4^n}$ Evaluate the limit $$\lim_{n\to\infty}\sqrt[\large n]{3^n + 4^n}.$$
Sorry, I'm not really sure how to find this limit. Can someone share a clever trick for this?

$$\lim_{n\to\infty}\sqrt[n]{3^n + 4^n}=\lim_{n \to \infty}\sqrt[n]{4^n \left ( \left (\frac{3}{4} \right )^n+1 \right )}=4 \lim_{n \to \infty}\sqrt[n] {\left (\frac{3}{4} \right )^n+1 }=4 \cdot 1=4 $$
