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Question : Induction Given the Fibonacci sequence: f, = 0 f, = 1 fn = fm + fra Prove by induction that f, plus the sum of the first n even Fibonacci numbers equals the (2n minus one)-th Fibonacci number: n f, + E f-2= f, + f +f,+f¸+.. + f -2 2i-2 2n-2 2n-1 i=1 Hint: You can do most of this problem without knowing the definition of the fibonacci sequence.

Question : Induction Given the Fibonacci sequence: f, = 0 f, = 1 fn = fm + fra Prove by induction that f, plus the sum of the first n even Fibonacci numbers equals the (2n minus one)-th Fibonacci number: n f, + E f-2= f, + f +f,+f¸+.. + f -2 2i-2 2n-2 2n-1 i=1 Hint: You can do most of this problem without knowing the definition of the fibonacci sequence.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question : Induction Given the Fibonacci sequence: f. = 0 f, = 1 fn = fr1 + fea Prove by induction that f, plus the sum of the first n even Fibonacci numbers equals the (2n minus one)-th Fibonacci number:. f, + £ fzi-2 + Σf. f. + f + f, + f¸ +...+ ƒ m-2= 2n-1 1 i=1 Hint: You can do most of this problem without knowing the definition of the fibonacci sequence.
Transcribed Image Text:Question : Induction Given the Fibonacci sequence: f. = 0 f, = 1 fn = fr1 + fea Prove by induction that f, plus the sum of the first n even Fibonacci numbers equals the (2n minus one)-th Fibonacci number:. f, + £ fzi-2 + Σf. f. + f + f, + f¸ +...+ ƒ m-2= 2n-1 1 i=1 Hint: You can do most of this problem without knowing the definition of the fibonacci sequence.
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