Theorem 43. Suppose (a;);2no is a constant sequence with value a. In other words, suppose a; = a for all i > no. Then (a;) converges to a. In other words, lim a = a.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 64E
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Prove Theorem 43.

Theorem 43. Suppose (a;)izno is a constant sequence with value a. In
other words, suppose a; = a for all i > no. Then (a;) converges to a. In
other words,
lim a = a.
i+00
Transcribed Image Text:Theorem 43. Suppose (a;)izno is a constant sequence with value a. In other words, suppose a; = a for all i > no. Then (a;) converges to a. In other words, lim a = a. i+00
Exercise 24 (Easy). Prove the above theorem. Hint, for all e > 0, the
choice N = no will work.
Transcribed Image Text:Exercise 24 (Easy). Prove the above theorem. Hint, for all e > 0, the choice N = no will work.
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