Jan 30, 2014 Thread starter #1 F Fermat Active member Nov 3, 2013 188 $Sup(\sum_{k=n+1}^{\infty}\frac{|x_{k}|^{2}}{4^{k}})$ where $x=(x_{1},x_{2},....)$ is in $l_{2}$ and the supremum is taken over all $x$ such that $||x||$=1. I think it is equal to $\frac{1}{4^{n+1}}$ Is this correct?

$Sup(\sum_{k=n+1}^{\infty}\frac{|x_{k}|^{2}}{4^{k}})$ where $x=(x_{1},x_{2},....)$ is in $l_{2}$ and the supremum is taken over all $x$ such that $||x||$=1. I think it is equal to $\frac{1}{4^{n+1}}$ Is this correct?