How to compute the limit $\lim_{n \to \infty} (1 + 2^n + 3^n +4^n+5^n)^{1/n}$?
My partial solution: $(1 + 2^n + 3^n +4^n+5^n)^{1/n} \leq (5 \times 5^n)^{1/n}$. Therefore $\lim_{n \to \infty} (1 + 2^n + 3^n +4^n+5^n)^{1/n} \leq \lim_{n \to \infty} 5^{(n+1)/n} = 5$.
Thank you very much.
