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Evaluating series Evaluate the following | Ch 8 - 17RE

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

Solution for problem 17RE Chapter 8

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 17RE

Evaluating series Evaluate the following infinite series or state that the series diverges.

Step-by-Step Solution:
Step 1 of 3

STEP_BY_STEP SOLUTION Step-1 Definition ; A series is said to be convergent if it approaches some limit .Formally , the infinite series a n is convergent if the sequence of partial sums n=1 n S n a k is convergent . Conversely , a series is divergent if the k=1sequence ofpartial sums is divergent.NOTE : The terms grow without bound , so the sequence does not converge. If U and V are convergent series , then ( U + V ) and ( U - V ) are k k k k k kconvergent . If C = / 0 , then U k and V k both converge or both diverge . Step-2a + ar + ar +ar +..................... is an infinite geometric progression.Here the first term is ‘a’ , and the common ratio is ‘r’ If |r| < 1 , then the sum of the series arn = a ……………(1) r=0 1 r rNOTE ; The infinite geometric series x converges if |x| < 1 , and diverges if |x| 1 r =0\n Step-3 3 3 The given sequence is S k ( 3k2 - 3k +1). k=1 n Then Sn= ( 3k2- 3k +1) k =1 = ( 3 - 3 + 3 - 3 + ………+ 3 - 3 + 3 - 3 ) 4 4 7 3n5 3n2 3n2 3n +1 3 1 = ( 3 - 3n+1 ) = 3(1 - 3n+1 ) . Therefore , S =n3(1 - 1 ) . 3n+1Now , we have to find the value of lim S = lim 3( 1 - 1 ) n n n 3n+1 = lim 3( 1 - 1 ). n n(3+ 1/n) 1 = 3(1-0) =3 , since as n , then 0.n 3 3 Therefore , ( 3k2 - 3k +1) = 3 . k=1 From the step(1) , step(2) , it is clear that the given infinite series is convergent . Becausethe value approaches to ‘3’ (finite value). 3 3 Therefore , ( 3k2- 3k +1) is convergent series. k=1

Step 2 of 3

Chapter 8, Problem 17RE is Solved
Step 3 of 3

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

This full solution covers the following key subjects: Series, diverges, evaluate, evaluating, infinite. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 17RE from 8 chapter was answered, more than 288 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 17RE from chapter: 8 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Evaluating series Evaluate the following infinite series or state that the series diverges.” is broken down into a number of easy to follow steps, and 13 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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Evaluating series Evaluate the following | Ch 8 - 17RE