How to evaluate $\displaystyle \lim_{n\to \infty}\left[a^n+b^n+c^n\right]^{1/n}$ What is the  $\displaystyle \lim_{n\to \infty}\left[a^n+b^n+c^n\right]^{1/n}$, assuming that $0<a<b<c$?
I think that, as 1/n tends to zero, the limit 1. Is this correct?

Hint:
Assuming that $0\le a\le b\le c$, then
$$(c^n)^{\frac{1}{n}}\le(a^n+b^n+c^n)^{\frac{1}{n}}\le(3c^n)^{\frac{1}{n}}$$
Now let $n\to\infty$,...
