Mathematical induction: Fibonacci numbers or Fibonacci sequence - H2 MATH - World Latest Movie, Series, Videos and Trailers | fetery.com

Mathematical induction: Fibonacci numbers or Fibonacci sequence

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Published on Jan 28, 2023

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Two recurrence formulas for the Fibonacci numbers are proven by mathematical induction. Define F_0=0, F_1=1, and F_k=F_{k-2}+F_{k-1} and the remaining terms for k greater than 1, that is, the F_k are defined by recurrence. The sequence (F_k) is called the Fibonacci sequence. This time it is proven that: F_{n-1}F_{n+1}=(F_n)^2+(-1)^n It is also proven that the sum of the first n terms squared is equal to F_nF_{n+1}.

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