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# Limits of sequences Evaluate the limit of the | Ch 8 - 9RE

ISBN: 9780321570567 2

## Solution for problem 9RE Chapter 8

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 9RE

2-10. Limits of sequences Evaluate the limit of the sequence or state that it does not exist.

$$a_{n}=\frac{(-1)^{n}}{0.9^{n}}$$

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 k and V k are convergent series , then ( U + Vk k ) and ( U - V k k ) areconvergent . If C = / 0 , then U k and V k both converge or both diverge . Step-2 (1) 1 nThe given sequence is a = n n = ( 0.9 (0.9) n = ( 10) , since 0.9 = 9 9 10 = ( 1) ( ) 10 n …………….(1) 9 10 10 n Here , 9 >1 . So , as n , then the value of ( ) 9 also tending to infinity. From the step (1) , we know that , The terms grow without bound , so the sequence does notconverge. n (1) n 10 n Therefore , lna =nlim n (0.9) = lin 1) ( ) 9 , since from (1).\n Therefore , the given sequence does not converge , since as n ,the termsgrow without bound . (1)n Therefore , lim a = lnm n does not converge. n n (0.9)

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##### ISBN: 9780321570567

This full solution covers the following key subjects: evaluate, exist, Limit, Limits, sequence. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. The answer to “?2-10. Limits of sequences Evaluate the limit of the sequence or state that it does not exist.$$a_{n}=\frac{(-1)^{n}}{0.9^{n}}$$” is broken down into a number of easy to follow steps, and 17 words. The full step-by-step solution to problem: 9RE from chapter: 8 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 9RE from 8 chapter was answered, more than 417 students have viewed the full step-by-step answer. 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.

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Limits of sequences Evaluate the limit of the | Ch 8 - 9RE