a lim - o Consider the following series. * (-1)* * 1 (jerror < 0.0000s) Show that the series is convergent. Since this series is an alternating series v , which condition(s) below show that it converges? (Select all that apply.) (n + 1)7 (n + 1)" In lim (n+ 1) How many terms of the series do we need to add in order to find the sum to the indicated accuracy? 13 x terms Enhanced Feedback Please try again, keeping in mind that you can apply the Alternating Series Test. First you can rewrite the nth term in the form (-1)"-Da where b,> 0, and then you need to verify the two conditions: (1) ba1 sb, for all n(i) lim b,-0 When both conditions are convergent; otherwise, the Alternating Series Test fails. To use the Alternating Series Estimation Theorem to estimate how many terms are needed to allow an error less then , you need to find the smallest integer n such that b+1 E.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 22RE
Question
Consider the following series.
Š (-1)^ + 1
n'
|error| < 0.00005
n = 1
Show that the series is convergent.
Since this series is an alternating series v
, which condition(s) below show that it converges? (Select all that apply.)
1
1
(n + 1)7
n7
1
1
(n + 1)7
n7
V lim
= 0
n- 0 n7
1.
lim
n-o (n + 1)7
How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
13
x terms
Enhanced Feedback
Please try again, keeping in mind that you can apply the Alternating Series Test. First you can rewrite the nth term in the form (-1)^-'b,, where b, > 0, and then you need to verify the two conditions: (i) b,+1 sb, for all n(ii) lim b, = 0 When both conditions are satisfied, the alternating series is
convergent; otherwise, the Alternating Series Test fails. To use the Alternating Series Estimation Theorem to estimate how many terms are needed to allow an error less then ɛ, you need to find the smallest integer n such that b,
n+1
<E.
Transcribed Image Text:Consider the following series. Š (-1)^ + 1 n' |error| < 0.00005 n = 1 Show that the series is convergent. Since this series is an alternating series v , which condition(s) below show that it converges? (Select all that apply.) 1 1 (n + 1)7 n7 1 1 (n + 1)7 n7 V lim = 0 n- 0 n7 1. lim n-o (n + 1)7 How many terms of the series do we need to add in order to find the sum to the indicated accuracy? 13 x terms Enhanced Feedback Please try again, keeping in mind that you can apply the Alternating Series Test. First you can rewrite the nth term in the form (-1)^-'b,, where b, > 0, and then you need to verify the two conditions: (i) b,+1 sb, for all n(ii) lim b, = 0 When both conditions are satisfied, the alternating series is convergent; otherwise, the Alternating Series Test fails. To use the Alternating Series Estimation Theorem to estimate how many terms are needed to allow an error less then ɛ, you need to find the smallest integer n such that b, n+1 <E.
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