Question

Give precise mathematical definitions or descriptions of each of the concept that follows. Then illustrate the definition or description with a graph or an algebraic example.

power series in$x-x_0$

Short answer

A power series is a collection of terms of the generic form$a_n{\left(x-x_0\right)}^n$

Step-by-step solution

Step 1. Given information

Concept is "power series in$x-x_0$"

Step 2. Explanation

In mathematics, a power series is an infinite series that can be thought of as a polynomial with an infinite number of terms.

A power series is a collection of terms of the generic form $a_n{\left(x-x_0\right)}^n$.

Graph of power series $f\left(x\right)=\frac{1}{1-x}$