Proof F(m+n) = F(m+1) * F(n) + F(m) * F(n-1) by Induction (Fibonacci Sequence)

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In this video we are going to proof the following property about the Fibonacci sequence: F(m+n) = F(m+1) * F(n) + F(m) * F(n-1) with the help with induction of m.

⏰ Timeline
00:00 Exercise
00:11 Base case
00:53 Induction hypothesis
01:07 Induction step
02:07 Base case #2
02:51 Induction hypothesis #2
03:07 Induction step

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Creative Commons — Attribution 3.0 Unported — CC BY 3.0
  1. Florian Ludewig
  2. fibonacci
  3. fibonacci proof
  4. proof by induction
  5. base case
  6. induction hypothesis
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Комментарии
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Great explanation, really helped me understand my homework!

TadeoSan
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I'm working on my homework related to Lucas Numbers, and I couldn't find much related to it. Thanks for your amazing explanation.. It helped me a lot!

Doppi-fjrx
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Can you do the induction process over n? I'm stuck trying to solve it...

jaimercosta
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or just use strong induction and assume that its true for m=1, 2, …, k and prove for m=k+1 i think its much easy this way

uncleilgaz