Hwk6_Solns - Math 3110 Spring 09 Homework 6: Selected...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Math 3110 Spring 09 Homework 6: Selected Solutions [8.2-1 (a, c, e)]: Claim : (a) X 1 x n 2 n n diverges at the right endpoint of its radius of con- vergence R = 2 and converges at the left endpoint of this interval. (b) X 1 x n n n diverges at both endpoints of its radius of convergence R = 1. (e) X 1 n + 2 n n x n diverges at both endpoints of its radius of convergence R = 1 Proof (a) Use the ratio test to determine that R = 2: lim n fl fl fl fl fl fl fl fl x n +1 2 n +1 n + 1 x n 2 n n fl fl fl fl fl fl fl fl = 1 2 lim n r n n + 1 | x | = 1 2 lim n r 1- 1 n + 1 ! | x | < 1 when | x | < 2. At x = 2, X 1 x n 2 n n = X 1 1 n , which diverges by comparison with the divergent p-series X 1 1 n . When x =- 2, we have an alternating series X 1 (- 1) n 1 n that converges by Cauchys Test since its terms a n = (- 1) n- 1 1 n go to zero in absolute value....
View Full Document

This note was uploaded on 11/09/2009 for the course MATH 3110 taught by Professor Ramakrishna during the Fall '08 term at Cornell University (Engineering School).

Page1 / 3

Hwk6_Solns - Math 3110 Spring 09 Homework 6: Selected...

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