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For wht values of p does converge

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 4E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 4E

For what values of p does \(\int_{1}^{\infty} x^{-p} d x\) converge?

Step-by-Step Solution:

Step 1 of 6

           

      Definition ;

                                     The    partial sum of the series  is given by

    =  +  ++..............+ . If the sequence of these partial sums {Sn} converges to L,

then the sum of the series converges to L. If {Sn} diverges, then the sum of the series diverges.

                   =     is  convergent  . Conversely  , a series is divergent if the sequence of partial sums is divergent. If    and   are convergent series , then   +  )   and  -   )    are convergent  . If  C ,  then  is convergent  series.

NOTE : The terms grow without bound ,  so the sequence does not converge.

 Integral test ; The series can be compared  to an integral to establish  convergence or divergence.

                       Let f(n) =  be a positive monotone decreasing function . If

                                         f(x) dx =   f(x) dx <  ,

then the series converges. But if the integral diverges, then the series does so as well.

 

Step 2 of 6

Chapter 7.7, Problem 4E is Solved
Step 3 of 6

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: converge, values, wht. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. The answer to “?For what values of p does \(\int_{1}^{\infty} x^{-p} d x\) converge?” is broken down into a number of easy to follow steps, and 11 words. The full step-by-step solution to problem: 4E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 4E from 7.7 chapter was answered, more than 445 students have viewed the full step-by-step answer.

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