/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 65 Prove that if x0鈭捯�,x0+蚁聽is ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q. 65 (page 671)

Prove that if x0鈭�蚁,x0+蚁is the interval of convergence for the series 鈭�k=0鈭�鈥�akx鈭�x0k, then the series converges conditionally at x0+p.

Short Answer

Expert verified

Ans: Therefore, the series converges conditionally atx0+p

Step by step solution

01

Step 1. Given formation.

given,

鈭�k=0鈭�鈥�akx鈭�x0k

02

Step 2. Consider the power series ∑k=0∞ akx−x0k and x0−ρ,x0+ρ is the interval of convergence of the series.

At x0+p, the series would become

鈭�k=0鈭�鈥�akx0+蚁鈭�x0k=鈭�k=0鈭�鈥�ak蚁k

This is precisely the series of absolute values when the original series is evaluated at x0+p

Therefore, the series converges conditionally at x0+p.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the interval of convergence for power series:鈭�k=0鈭�-1k2k+1x2k+1

Why is it helpful to know the Maclaurin series for a few basic functions?

In Exercises 49鈥�56 find the Taylor series for the specified function and the given value of x0. Note: These are the same functions and values as in Exercises 41鈥�48.

51.sinx,蟺

Find the interval of convergence for each power series in Exercises 21鈥�48. If the interval of convergence is finite, be sure to analyze the convergence at the endpoints.

鈭�k=0鈭�-1kk23kx-12k

In Exercises 49鈥�56 find the Taylor series for the specified function and the given value of x0. Note: These are the same functions and values as in Exercises 41鈥�48.

role="math" localid="1649406173168" 49.cosx,蟺2
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.