# Embarcadero Delphi 2010 Serial Number

Embarcadero Delphi 2010 Serial Number Embarcadero Delphi 2010 Serial Number

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Calculate $B_a(E)$

The set $E$ is the set of all real numbers $x$ for which the series $\sum_{n=1}^{\infty} \frac{1}{3^n}$ converges. Describe $B_a(E)$ where $a=0$ and $a=\frac{1}{2}$.

I’m not really sure how to approach this. I know $a$ would give me the radius of convergence of the series, and I know it converges, but how do I use that to calculate $B_a(E)$?

A:

Your knowledge of the definition of the balls is good.
With $r=\frac{1}{2}$, we have $$\forall x\in E,\,\left|x-\frac{1}{2}\right|=\frac{1}{2}-\left(\frac{1}{2}-x\right)=-x-\frac{1}{2}=-x-\frac{1}{2}-\left|x\right|=x+\left|x\right|$$
and you can do then the following calculations: