2. The Fibonacci sequence, first studied by the thirteenth century Italian mathematician Leonardo di Pisa, also known as Fibonacci, is defined recursively by Fn = Fn-1+ Fn-2 for n > 2 and F1 = 1, F2 = 1. (a) Find the first 10 terms. (b) At each step n, take the list of the first n Fibonacci numbers and, if possible, split it into two lists such that the sum of the numbers in each list is the same. For example, when n = 3, we have the list {1,1, 2}. This list can be split into two lists with equal sums: {1,1}, and {2}. But, when n = 1, the original list has only one number, {1}, and this can't be split into two equal done: always, never, only for certain n? Discover as much as you can.
2. The Fibonacci sequence, first studied by the thirteenth century Italian mathematician Leonardo di Pisa, also known as Fibonacci, is defined recursively by Fn = Fn-1+ Fn-2 for n > 2 and F1 = 1, F2 = 1. (a) Find the first 10 terms. (b) At each step n, take the list of the first n Fibonacci numbers and, if possible, split it into two lists such that the sum of the numbers in each list is the same. For example, when n = 3, we have the list {1,1, 2}. This list can be split into two lists with equal sums: {1,1}, and {2}. But, when n = 1, the original list has only one number, {1}, and this can't be split into two equal done: always, never, only for certain n? Discover as much as you can.
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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Transcribed Image Text:2. The Fibonacci sequence, first studied by the thirteenth century Italian mathematician Leonardo di
Pisa, also known as Fibonacci, is defined recursively by
Fn = Fn-1+ Fn-2 for n > 2 and F1 = 1, F2 = 1.
(a) Find the first 10 terms.
(b) At each step n, take the list of the first n Fibonacci numbers and, if possible, split it into two
lists such that the sum of the numbers in each list is the same. For example, when n = 3, we
have the list {1,1, 2}. This list can be split into two lists with equal sums: {1,1}, and {2}. But,
when n = 1, the original list has only one number, {1}, and this can't be split into two equal
done: always, never, only for certain n? Discover as much as you can.
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