Problem 7.4.7. (a) Prove that if lim,→∞ 8n = 8 and s < t, then there exists a real number N such that if n > N then sn < t. (b) Prove that if lim,00 8n = s and r < s, then there exists a real number M such that if n > M then r < sn.
Problem 7.4.7. (a) Prove that if lim,→∞ 8n = 8 and s < t, then there exists a real number N such that if n > N then sn < t. (b) Prove that if lim,00 8n = s and r < s, then there exists a real number M such that if n > M then r < sn.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 25E
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![Problem 7.4.7.
(a) Prove that if limn→∞ Sn
= s and s <t,
then there exists a real number N such
that if n > N then s, < t.
< t.
(b) Prove that if limn Sn = s and r < s,
then there exists a real number M such
that if n > M then r < sn:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0335de1d-d88b-4764-a43c-e2195c6bbbda%2F37078791-6ed6-4421-82e1-5cd04a4ad3b7%2Fful4pgc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 7.4.7.
(a) Prove that if limn→∞ Sn
= s and s <t,
then there exists a real number N such
that if n > N then s, < t.
< t.
(b) Prove that if limn Sn = s and r < s,
then there exists a real number M such
that if n > M then r < sn:
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