Show that lim(p-> infinity) ||x||p = ||x||∞ for all x in Rn
Here's a hint. Write (and justify) $\displaystyle \left(\max_{1\leq i\leq n} |x_i|\right)^p\leq |x_1|^p+\cdots+|x_n|^p\leq n\left(\max_{1\leq i\leq n} |x_i|\right)^p$. (Note: it would have been nice to know what you already tried to do in addition of just stating your question)