Prove without using induction that Fn+1^2 - Fn^2 = Fn-1 * F n+2 where F represents a Fibonacci number. Please show all steps, especially how multiplying (Fn+1 - Fn) * (Fn+1 - Fn) on the LHS equals Fn-1 * F n+2.
Prove without using induction that Fn+1^2 - Fn^2 = Fn-1 * F n+2 where F represents a Fibonacci number. Please show all steps, especially how multiplying (Fn+1 - Fn) * (Fn+1 - Fn) on the LHS equals Fn-1 * F n+2.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 35E
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Prove without using induction that
Fn+1^2 - Fn^2 = Fn-1 * F n+2
where F represents a Fibonacci number. Please show all steps, especially how multiplying (Fn+1 - Fn) * (Fn+1 - Fn) on the LHS equals Fn-1 * F n+2. Thank you!!!
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