Binet’s Formula The following formula is known as Binet's formula for the n th Fibonacci number. F n = 1 5 [ ( 1 + 5 2 ) n − ( 1 − 5 2 ) n ] The advantage of this formula over the recursive formula F n = F n − 1 + F n − 2 is that you can determine the n th Fibonacci number without finding the two pre- ceding Fibonacci numbers. Use Binet’s formula and a calculator find the 20th. 30th, and 40th Fibonacci numbers.
Binet’s Formula The following formula is known as Binet's formula for the n th Fibonacci number. F n = 1 5 [ ( 1 + 5 2 ) n − ( 1 − 5 2 ) n ] The advantage of this formula over the recursive formula F n = F n − 1 + F n − 2 is that you can determine the n th Fibonacci number without finding the two pre- ceding Fibonacci numbers. Use Binet’s formula and a calculator find the 20th. 30th, and 40th Fibonacci numbers.
Binet’s Formula The following formula is known as Binet's formula for the nth Fibonacci number.
F
n
=
1
5
[
(
1
+
5
2
)
n
−
(
1
−
5
2
)
n
]
The advantage of this formula over the recursive formula
F
n
=
F
n
−
1
+
F
n
−
2
is that you can determine the nth Fibonacci number without finding the two pre- ceding Fibonacci numbers.
Use Binet’s formula and a calculator find the 20th. 30th, and 40th Fibonacci numbers.
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