9. Define a sequence a1, a2, a3, ... as follows: a₁ = 1, a2 = 3, and akak-1+ak-2 for all integers k ≥ 3. (This sequence is known as the Lucas sequence.) Use strong mathematical induction to prove that a, ≤ (7)" for all integers n ≥ 1. 10. The problem that as used to introduce rdinary mathe

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9. Define a sequence a1, a2, a3, ... as follows: a₁ = 1, a2 = 3,
and akak-1+ak-2 for all integers k ≥ 3. (This sequence
is known as the Lucas sequence.) Use strong mathematical
induction to prove that a, ≤ (7)" for all integers n ≥ 1.
10. The problem that as used to introduce rdinary mathe
Transcribed Image Text:9. Define a sequence a1, a2, a3, ... as follows: a₁ = 1, a2 = 3, and akak-1+ak-2 for all integers k ≥ 3. (This sequence is known as the Lucas sequence.) Use strong mathematical induction to prove that a, ≤ (7)" for all integers n ≥ 1. 10. The problem that as used to introduce rdinary mathe
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