# Question regarding Power Series

## Homework Statement

It is stated in my textbook that the sum ## \sum_{0}^{\infty} 8^{-n}(x^2-1)^n ## is not a power series but can be turned into one using he substitution ##y=x^2-1## which then becomes the power series ##\sum_{0}^{\infty} 8^{-n}y^n ## They aren't offering any explanation as to why and I have evaluated the interval on which the series converges and it gives the same result regardless of whether or not the substitution is used. I guess what I'm wondering is why isn't the first sum a power series?

## The Attempt at a Solution

The x2 inside the parenthesis makes it not a power series. A power series must have x1 inside the parenthesis.

The x2 inside the parenthesis makes it not a power series. A power series must have x1 inside the parenthesis.
Okay thanks for the information.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
Well, technically it is a power series in ##x^2-1##.

Ray Vickson