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Let {an}-1 be a positive sequence which satisfies nan+1 < an for all n > 1. Prove that > an converges n=1 a1 Prove that a,n < for all n > 1. (п — 1)! 8. Given that a1 = 137 and e = Σ (for any x E R), find M so that >an < M. n! n=0 n=1 IM:

Let {an}-1 be a positive sequence which satisfies nan+1 < an for all n > 1. Prove that > an converges n=1 a1 Prove that a,n < for all n > 1. (п — 1)! 8. Given that a1 = 137 and e = Σ (for any x E R), find M so that >an < M. n! n=0 n=1 IM:

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
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Let {an}1 be a positive sequence which satisfies nan+1< an for all n > 1. z=1 Prove that > An converges n=1 a1 Prove that an < for all n > 1. (n – 1)! Given that ai = 137 and et (for any x E R), find M so that > An < M. n! n=0 n=1
Transcribed Image Text:Let {an}1 be a positive sequence which satisfies nan+1< an for all n > 1. z=1 Prove that > An converges n=1 a1 Prove that an < for all n > 1. (n – 1)! Given that ai = 137 and et (for any x E R), find M so that > An < M. n! n=0 n=1
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