Proficiency #11. [Induction] Let Fn be the Fibonacci numbers, given by F1 = 1, F2 = 1, and for all integers n > 1, Fn+2 = Fn+1+ Fn. Prove that for all integers n > 1, %3D 2n > FR-1 FR = F,F2 + F2F3 +...

Proficiency #11. [Induction]<br>Let Fn be the Fibonacci numbers, given by F1 = 1, F2 = 1, and for all integers n > 1,<br>Fn+2 = Fn+1+ Fn. Prove that for all integers n > 1,<br>%3D<br>2n<br>> FR-1 FR = F,F2 + F2F3 + · …· + F2n-2F2n-1+ F2n-1F2n = F.<br>k=2<br>

Extracted text: Proficiency #11. [Induction] Let Fn be the Fibonacci numbers, given by F1 = 1, F2 = 1, and for all integers n > 1, Fn+2 = Fn+1+ Fn. Prove that for all integers n > 1, %3D 2n > FR-1 FR = F,F2 + F2F3 + · …· + F2n-2F2n-1+ F2n-1F2n = F. k=2

Jun 04, 2022

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Proficiency #11. [Induction] Let Fn be the Fibonacci numbers, given by F1 = 1, F2 = 1, and for all integers n > 1, Fn+2 = Fn+1+ Fn. Prove that for all integers n > 1, %3D 2n > FR-1 FR = F,F2 + F2F3 +...

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