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. i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3. ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge. .

. i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3. ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge. .

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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E. i. Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3.
ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.

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E. i. Suppose that the s, satisfies both limn- $2n = 3 and limn- $2n+1 = 3. (That is, the sequence given by the even terms of s, and that given by the odd terms of s, both converge to 3.) Show that also limn-co Sn = 3. ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.
Transcribed Image Text:E. i. Suppose that the s, satisfies both limn- $2n = 3 and limn- $2n+1 = 3. (That is, the sequence given by the even terms of s, and that given by the odd terms of s, both converge to 3.) Show that also limn-co Sn = 3. ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.
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