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:
$\begin{array}{|l|l|}\hline&\begin{cases}a=0\\x\in E\end{cases}\quad&\begin{cases}a=1\\x\in E\end{cases}\\\hline\\
x\in E&0\leqslant\left|x\right|\le
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Let y = 2 + 3. Let j(q) = 0*q**3 – q**3 + 5*q**2 – 4*q**2 + q – 2*q**2. Let s(h) = -5*h**3 – 5*h**2 + 2*h + 2. Let b(d) = -6*j(d) + s(d). Determine b(y).
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Embarcadero Delphi 2010 serial number
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