15. We define a sequence of integers as follows: fo fi fn = = 0, 1, fn-1 + fn-2 = for n ≥ 2. The integer fr is called the nth Fibonacci number. Compute the Fi- bonacci numbers fn for n = = 2,3,..., 12. Prove that (fn, fn+1) = 1 for all nonnegative integers n.
15. We define a sequence of integers as follows: fo fi fn = = 0, 1, fn-1 + fn-2 = for n ≥ 2. The integer fr is called the nth Fibonacci number. Compute the Fi- bonacci numbers fn for n = = 2,3,..., 12. Prove that (fn, fn+1) = 1 for all nonnegative integers n.
Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:15. We define a sequence of integers as follows:
fo
f₁
fn
=
=
0,
1,
fn-1 + fn-2
=
for n ≥ 2.
The integer fn is called the nth Fibonacci number. Compute the Fi-
bonacci numbers fn for n = = 2,3,..., 12. Prove that (fn, fn+1) = 1
for all nonnegative integers n.
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