5. Problem 5.26 from the text, which I reproduce here. Problem 5.26. The Fibonacci numbers Fo. F1. F2.... are defined as follows: if n = 0. Fn if n = 1. Fn-1 + Fn-2 if n> 1. These numbers satisfy many unexpected identities, such as F공+ 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 hase case (n
5. Problem 5.26 from the text, which I reproduce here. Problem 5.26. The Fibonacci numbers Fo. F1. F2.... are defined as follows: if n = 0. Fn if n = 1. Fn-1 + Fn-2 if n> 1. These numbers satisfy many unexpected identities, such as F공+ 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 hase case (n
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:5. Problem 5.26 from the text, which I reproduce here.
Problem 5.26.
The Fibonacci numbers Fo. F1, F2.... are defined as follows:
if n = 0,
Fn ::=
if n = 1.
Fn-1 + Fn-2 if n > 1.
These numbers satisfy many unexpected identities, such as
F + F? ++ F = F, Fn+1
(5.22)
...
%3D
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).
%3D
(b) Now prove the
inductive step.
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