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Supremum of series

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?