What is the fibonacci sequence who invented it and what is it used for

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Step-by-step explanation:

- The Fibonacci Sequence is the series of numbers:

 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

- The next number is found by adding up the two numbers before it

# Example:

- The 2 is found by adding the two numbers before it (1+1)

- The 3 is found by adding the two numbers before it (1+2),

- The 5 is (2+3) and so on

- The rule of it is x(n) = x(n-1) + x(n-2) where

# x(n) is term number ⇒ n

# x(n-1) is the previous term ⇒ (n-1)

# x(n-2) is the term before that ⇒ (n-2)

- Example: the 8th term is  the 7th term plus the 6th term:

 x(8) = x(7) + x(6)

# Note: When we take any two consecutive Fibonacci Numbers,

 their ratio is very close to the Golden Ratio φ

- The Golden Ratio φ is approximately 1.618034...

- We can calculate any Fibonacci Number using the Golden Ratio:

  x(n) = [φ^n - (1 - φ)^n]/√5

- The answer is a whole number, exactly equal to the addition of the

  previous two terms.

# There is an interesting patterns in Fibonacci sequence:

  every nth number is a multiple of x(n)

- Example:

* x3 = 2 ⇒ every 3rd number is a multiple of 2 (2, 8, 34, 144, 610, ...)

* x4 = 3 ⇒ Every 4th number is a multiple of 3 (3, 21, 144, ...)

* x5 = 5 ⇒ Every 5th number is a multiple of 5 (5, 55, 610, ...)

- The man who invented it.

 His real name was Leonardo Pisano Bogollo, and he lived between

 1170 and 1250 in Italy.

- Fibonacci was his nickname

- Fibonacci sequence is it used for:

# Reflects patterns of growth spirals (a spiral curve , shape , pattern ,

  object) found in nature

# It is the closest approximation in integers to the logarithmic spiral

  series, which follows the same rule as the Fibonacci sequence

, ; dcbsdkmnld

step-by-step explanation:

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.