chap11sec8

chap11sec8 - 11.8 Power Series

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
11.8 Power Series Many familiar (and unfamiliar) functions can be written in the form  2 3 0 1 2 3 c c x c x c x + + + + L  as an infinite sum  of the product of certain numbers  n c  and powers of the variable  x . Such expressions are called  power series with center 0; the numbers  n c  are called its coefficients,  0 n n n c x = . Slightly more general, an expression of the form  2 0 1 2 ( ) ( ) c c x a c x a + - + - + L  is called a  power series in (x-a) or a  power series centered at a,   0 ( ) n n n c x a = - . So, the question becomes, "when does the power series converge?" Any of the series tests are available for use, but most often the  Ratio Test is used. In general this will boil down to  1 lim n n n c x a c + →∞ - When this limit is between –1 and 1, the series  converges. There are only 3 possibilities for how this series can converge.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

chap11sec8 - 11.8 Power Series

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online