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.
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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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