Question

What is a power series in x?

Short answer

A power series in x is$\sum _{k=0}^{\infty }{a}_k{x}^k$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

x

Step 2. Determine a power series in x.

If $\sum _{k=0}^{\infty }{a}_k$ is a sequence of real numbers and x is a variable.

Then a power series in x is a series of the form $\sum _{k=0}^{\infty }{a}_k{x}^k$.

Rewriting the series,

$\sum _{k=0}^{\infty }{a}_k{x}^k=a_0+a_{1}x+a_2{x}^2+...$