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lakkis [162]
3 years ago
13

Fibonacci numbers can be found in many places in nature, for example, the number of petals in a daisy, the number of spirals in

a pine cone or a pineapple, and even the way branches grow on a tree. Find an example of something natural where you can see a Fibonacci number in action, and sketch it here.

Mathematics
1 answer:
Otrada [13]3 years ago
4 0

Answer: The Fibonacci sequence is a numerical pattern that can appear in many living things. It was first described in the 12th century by the Italian Leonardo Finonacci.

It is an infinite sequence that begins with 0 and 1. The sequence is completed with the sum of the previous 2 numbers.

Following this logic, we can assemble the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on.

This sequence is very common in nature and can be observed in many living things, such as insects, plants, the human face, even a chameleon's tail.

For example in a shell.

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\displaystyle
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<em>-------------------------------------------------------------</em>


\displaystyle&#10;(x^2+y)^n=\sum_{k=0}^n\binom{n}{k}x^{2n-2k}y^k\\&#10;n=5\\&#10;k=3\\\\\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdor5}{2}=10

<u>It's 10.</u>

----------------------------------------------------

\displaystyle&#10;(3x^2+y)^n=\sum_{k=0}^n\binom{n}{k}(3x)^{2n-2k}y^k=\sum_{k=0}^n\binom{n}{k}\cdot 3^{2n-2k}\cdot x^{2n-2k}y^k\\\\&#10;n=5\\&#10;k=4\\\\&#10;\binom{5}{3}\cdot3^{2\cdot5-2\cdot4}=10\cdot3^{2}=10\cdot9=90

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