I am having trouble proving this.
Prove that lim$_{p→∞}$ ||v ||$_p$ = ||v||$_∞$ for any v $\in$ $R^2$.
My attempt:
We have that ||v ||$_p$ = p (∑||v$_i$||p)^1/2 from the interval of i=1 to infinity,which equals to ||v ||$_p$ = (|v$_1$| + |v$_2$| ... + |v$_n$|) but from here on how can I show that it is equal to ||v||$_∞$. It seems very obvious it is, but how can I show it formally?
Note: Sorry for my coding format. I am very bad at it.