Recall the Fibonacci sequence: f₁ = 1 f2 = 1 fn = fn-1 + fn-2, for n ≥ 3 Prove by strong induction that for any integer n ≥ 1, (1+√5)n-(1-√5)n √5 fn

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
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Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 70SE: Calculate the first eight terms of the sequences an=(n+2)!(n1)! and bn=n3+3n32n , and then make a...
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Problem 2
Recall the Fibonacci sequence:
f₁ = 1
f2 = 1
fn = fn-1 + fn-2, for n ≥ 3
Prove by strong induction that for any integer n ≥ 1,
(1+√5)n- (1-√5)n
√5
fn=
Transcribed Image Text:Problem 2 Recall the Fibonacci sequence: f₁ = 1 f2 = 1 fn = fn-1 + fn-2, for n ≥ 3 Prove by strong induction that for any integer n ≥ 1, (1+√5)n- (1-√5)n √5 fn=
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