Chapter 8.5, Problem 1E

To determine

To find: The definition of power series.

Answer to Problem 1E

In mathematics, a power series is an infinite series of the form where $a_n$ represents the coefficient of the $n^{th}$ term and c is a constant .

  $a_n$ is independent of $x$ and may be expressed as a function of $n$ .

Explanation of Solution

Given information: A power series.

Calculation: The definition of power series is,

In mathematics, a power series is an infinite series of the form where $a_n$ represents the coefficient of the $n^{th}$ term and c is a constant .

  $a_n$ is independent of $x$ and may be expressed as a function of $n$ .

Example: ${{\displaystyle \sum _{n=0}^{\infty }{c}_n\left(x-a\right)}}^n$