/*! 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 47. Find the interval of convergence... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Q 47. (page 670)

Find the interval of convergence for power series:鈭�k=0鈭�1kkx-3k

Short Answer

Expert verified

The interval of convergence for power series isR.

Step by step solution

01

Step 1. Given information. 

The given power series is鈭�k=0鈭�1kkx-3k.

02

Step 2. Find the interval of convergence.  

Here we use modified root test for the series. This is reasonable choice for the series because the factors of the terms of the series involves kthpower.

Let us take bk=1kkx-3k

Thus, limk鈫�鈭�bkk=limk鈫�鈭�1kkx-3kk=limk鈫�鈭�1kx-3

Now, we evaluating the preceding limit as k鈫�鈭�.No matter what the variable xtakes on the limit is zero.

That is limk鈫�鈭�1kx-3=0

Therefore, by the modified root test the series converges absolutely for every value of x.

Thus, the interval of the convergence isR.

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

In Exercises 41鈥�48 find the fourth Taylor polynomial P4(x)for the specified function and the given value of x0.

48.sin3x,蟺6

In Exercises 23鈥�32 we ask you to give Lagrange鈥檚 form for the corresponding remainder, R4(x)

ln(1+x)

If m is a positive integer, how can we find the Maclaurin series for the function f(cxm)if we already know the Maclaurin series for the function f(x)? How do you find the interval of convergence for the new series?

What is a Taylor polynomial for a function f at a point x0?

Find the interval of convergence for power series:鈭�k=0鈭�k+13k2x-5k
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

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.