4. Let a1 = 1 and an+1 = (an + 1) for n>1. (a) Find a2, az and a4. (b) Use induction to show that an > for all n. (c) Show that (an) is a convergent sequence and compute its limit.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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Please solve b
4. Let a1
= 1 and an+1 = (an + 1) for n> 1.
(a) Find a2, az and a4.
(b) Use induction to show that an > for all n.
(c) Show that (an) is a convergent sequence and compute its limit.
Transcribed Image Text:4. Let a1 = 1 and an+1 = (an + 1) for n> 1. (a) Find a2, az and a4. (b) Use induction to show that an > for all n. (c) Show that (an) is a convergent sequence and compute its limit.
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