i. For a convergent real sequence sn and a real number a, show that if sna for all but finitely many values of n, then limm- Sn za. ii. For each value of a € R, give an example of a convergent sequences with sna for all n, but where limn-Sn = a.

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 55E
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E.
i. For a convergent real sequences, and a real number a, show that if 5, Za for all but finitely many values of n, then lim,-. Sn z a.
ii. For each value of a € R, give an example of a convergent sequences, with sn> a for all n, but where lim-Sn = a.
Transcribed Image Text:E. i. For a convergent real sequences, and a real number a, show that if 5, Za for all but finitely many values of n, then lim,-. Sn z a. ii. For each value of a € R, give an example of a convergent sequences, with sn> a for all n, but where lim-Sn = a.
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