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Intertraff ANPR Engine100 SDK V1.22.2.0

Intertraff ANPR Engine100 SDK V1.22.2.0


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Intertraff ANPR Engine100 SDK V1.22.2.0

Intertraff ANPR Engine100 SDK v1.22.2.0 – The ANPR Engine SDK is a set of software development tools that allows application developers to integrate our .Q:

Power series formalizing a function $f(x)$

I am trying to formalize a function $f$ of one variable.
Defining $f : \mathbb{R} \to \mathbb{R}$ by
$$f(x) = \frac{1}{1-x}$$
I want to ask if

$f$ is a power series.
$f$ is a power series with radius of convergence $=1$.

That is, I want to check if there is a (finite) series
$$\sum_{k=0}^\infty c_k x^k$$
such that:
$$f(x) = \sum_{k=0}^\infty c_k x^k$$
I tried using the Lagrange Inequality to show that $|c_k| \leq \frac{1}{k+1}$ for $k \geq 1$ and therefore,
$$\sum_{k=0}^\infty c_k x^k \leq \sum_{k=0}^\infty \frac{x^k}{k+1} = \sum_{k=0}^\infty \frac{x^k}{k!}$$
and, since the series on the right is convergent for $0 \leq x 1$, then the series on the left converges for $0 \leq x \leq 1$ and diverges for $x > 1$.
I am having trouble showing that $c_0 = \frac{1}{2}$.
I would like a more formal approach to show that $c_0 = \frac{1}{2}$ and the radius of convergence is $1$ if that is what is needed.

A:

Rewrite the definition of $f$ as
$$ f(x) = \frac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots$$
We know that the partial sums of this series converge to $f$ on every compact subset of $[

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Intertraffic anpr engine 100. Intertraffic ANPR Engine100 SDK V1.22.2.0. Some side effects may occur when upgrading to this version. .
intertraffic anpr engine 100. Intertraffic ANPR Engine100 SDK V1.22.2.0. Some side effects may occur when upgrading to this version. .
Intertraffic ANPR Engine 100 SDK v1.22.2.0 – [ Update ]… · Intertraffic ANPR Engine 100 SDK v1.22.2.0. Some side effects may occur when upgrading to this version.
Intertraffic ANPR Engine 100 SDK V1.22.2.0. – [ Update ]… · Intertraffic ANPR Engine 100 SDK v1.22.2.0. Some side effects may occur when upgrading to this version.
Intertraffic ANPR Engine 100 SDK V1.22.2.0- [ Update ]… · Intertraffic ANPR Engine 100 SDK v1.22.2.0. Some side effects may occur when upgrading to this version.
Intertraffic ANPR Engine 100 SDK V1.22.2.0 – [ Update ]… · Intertraffic ANPR Engine 100 SDK v1.22.2.0. Some side effects may occur when upgrading to this version.
Intertraffic ANPR Engine 100 SDK V1.22.2.0. – [ Update ]… · Intertraffic ANPR Engine 100 SDK v1.22.2.0. Some side effects may occur when upgrading to this version.
Read Review Latest Update, .
[ Update ]… · Intertraffic ANPR Engine 100 SDK v1.22.2.0. Some side effects may occur when upgrading to this version.
Intertraffic ANPR Engine 100 SDK V1.22.2.0- [ Update ]… · Intertra
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