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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc15a1b2c-f20f-4021-9e6b-69b0dda6429d%2F30f12c06-fde8-4126-8fe0-d03cf092941d%2Fcjr9v5g_processed.png&w=3840&q=75)
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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