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1 -2 3 -4 2' 5'8' 1l general term, an of the sequence. 5. (a) Consider the sequence Give a rule for obtaining the

1 -2 3 -4 2' 5'8' 1l general term, an of the sequence. 5. (a) Consider the sequence Give a rule for obtaining the

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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1 -2 3 -4 2 5 8' 11 5. (a) Consider the sequence Give a rule for obtaining the general term, an of the sequence. (b) A sequence an is said to converge to a real number a* provided for each e> 0, 3 n(e) E N, such that V n EN, n> n(e), implies |an – a*| < €. Let Vn > 1. Show that lim,n+ An = 1 an be a sequence defined by an = n +1' and prove your assertion. (c) Let a, be a convergent sequence in R. Prove that a, is bounded. (d) Let a, b e R. If Ja < b then -b < a <b. Find all values r ER that satisfy the inequality |r2 – 1| < 3.
Transcribed Image Text:1 -2 3 -4 2 5 8' 11 5. (a) Consider the sequence Give a rule for obtaining the general term, an of the sequence. (b) A sequence an is said to converge to a real number a* provided for each e> 0, 3 n(e) E N, such that V n EN, n> n(e), implies |an – a*| < €. Let Vn > 1. Show that lim,n+ An = 1 an be a sequence defined by an = n +1' and prove your assertion. (c) Let a, be a convergent sequence in R. Prove that a, is bounded. (d) Let a, b e R. If Ja < b then -b < a <b. Find all values r ER that satisfy the inequality |r2 – 1| < 3.
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