Question

use power series operations to find the taylor series at ( x = 0 ) for the following function.

( \frac { 64 } { ( 1 - x ) ^ { 2 } } )

the taylor series for ( \frac { 1 } { 1 - x } ) is a commonly known series. what is the taylor series at ( x = 0 ) for ( \frac { 1 } { 1 - x } )?

( sum _ { n = 0 } ^ { infty } square ) (type an exact answer.)

Explanation:

Step1: Recall the geometric series formula

The geometric series formula is \(\frac{1}{1 - x}=\sum_{n = 0}^{\infty}x^{n}\), for \(|x|<1\).

Answer:

\(\sum_{n = 0}^{\infty}x^{n}\)