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Problem 5.26. The Fibonacci numbers Fo, F1, F2,... are defined as follows: if n = 0, if n = 1, Fn-1 + Fn-2 if n > 1. Fn := {1 These numbers satisfy many unexpected identities, such as F + F{ + ...+ F: = F„Fn+1 (5.22) Equation (5.22) can be proved to hold for all n e N by induction, using the equation itself as the induction hypothesis, P(n). (a) Prove the base case (n = 0). (b) Now prove the inductive step.

Problem 5.26. The Fibonacci numbers Fo, F1, F2,... are defined as follows: if n = 0, if n = 1, Fn-1 + Fn-2 if n > 1. Fn := {1 These numbers satisfy many unexpected identities, such as F + F{ + ...+ F: = F„Fn+1 (5.22) Equation (5.22) can be proved to hold for all n e N by induction, using the equation itself as the induction hypothesis, P(n). (a) Prove the base case (n = 0). (b) Now prove the inductive step.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Problem 5.26. The Fibonacci numbers Fo, F1, F2,... are defined as follows: if n = 0, if n = 1, Fn-1 + Fn-2 if n > 1. Fn := {1 These numbers satisfy many unexpected identities, such as F + F{ + ...+ F: = F„Fn+1 (5.22) Equation (5.22) can be proved to hold for all n e N by induction, using the equation itself as the induction hypothesis, P(n). (a) Prove the base case (n = 0). (b) Now prove the inductive step.
Transcribed Image Text:Problem 5.26. The Fibonacci numbers Fo, F1, F2,... are defined as follows: if n = 0, if n = 1, Fn-1 + Fn-2 if n > 1. Fn := {1 These numbers satisfy many unexpected identities, such as F + F{ + ...+ F: = F„Fn+1 (5.22) Equation (5.22) can be proved to hold for all n e N by induction, using the equation itself as the induction hypothesis, P(n). (a) Prove the base case (n = 0). (b) Now prove the inductive step.
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