Homework Help is Here – Start Your Trial Now!
Math
Calculus
. 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. .

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
See similar textbooks
icon
Related questions
Question

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.

.
 
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.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS