A sequence {a} is defined recursively 1, an+1 = √an +6, n ≥1 by a₁ = 1 a) Use Mathematical Induction to prove that an <3 for all n b) Show that an+1 > an for all n
A sequence {a} is defined recursively 1, an+1 = √an +6, n ≥1 by a₁ = 1 a) Use Mathematical Induction to prove that an <3 for all n b) Show that an+1 > an for all n
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 32E
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1, an+1 = √an +6, n ≥1
by a₁ = 1
a) Use Mathematical Induction to prove
that an <3 for all n
b) Show that an+1 > an for all n"
Transcribed Image Text:A sequence {a} is defined recursively
1, an+1 = √an +6, n ≥1
by a₁ = 1
a) Use Mathematical Induction to prove
that an <3 for all n
b) Show that an+1 > an for all n
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