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

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
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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
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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