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The limit of the ratio is the Golden ratio, or [1 + sqrt(5)]/2

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โˆ™ 2009-12-10 19:41:16
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Q: What is the limit of the ratio of consecutive terms of the Fibonacci sequence?
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Is the Fibonacci sequence the golden ratio?

No, but the ratio of each term in the Fibonacci sequence to its predecessor converges to the Golden Ratio.


What is the relationship between the golden ratio and the standard Fibonacci sequence?

The "golden ratio" is the limit of the ratio between consecutive terms of the Fibonacci series. That means that when you take two consecutive terms out of your Fibonacci series and divide them, the quotient is near the golden ratio, and the longer the piece of the Fibonacci series is that you use, the nearer the quotient is. The Fibonacci series has the property that it converges quickly, so even if you only look at the quotient of, say, the 9th and 10th terms, you're already going to be darn close. The exact value of the golden ratio is [1 + sqrt(5)]/2


Does the limit exist for fn divided by fn-1 in the Fibonacci sequence and if so what is it?

The limit is the Golden ratio which is 0.5[1 + sqrt(5)]


What is the ratio of the sequence?

The answer depends on the sequence. The ratio of terms in the Fibonacci sequence, for example, tends to 0.5*(1+sqrt(5)), which is phi, the Golden ratio.


How is the golden ratio devised?

The 'golden ratio' is the limit of the ratio of two consecutive terms of the Fibonacci series, as the series becomes very long. Actually, the series converges very quickly ... after only 10 terms, the ratio of consecutive terms is already within 0.03% of the golden ratio.


What are the relations between the golden ratio and the Fibonacci series?

The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.


How does the golden ratio relate to the Fibonacci sequence?

The golden ratio is approximately 1.618: 1. This ratio is commonly found in nature and architecture. Stock traders often look for this ratio in patterns on stock charts. One way to compute this ratio is to compare any adjacent Fibonacci numbers. For this reason stock traders often refer to this type of analysis using the term Fibonacci, as in "Fibonacci retracements".


In a geometric sequence the between consecutive terms is constant.?

Ratio


How is Lenardo Fibonacci discoverey used in science?

Your mind will be blown if you search Phi, The golden ratio, or the fibonacci sequence. It has to do with everything.


When and how is the Fibonacci Sequence used?

The Fibonacci sequence can be used to give ever increasing accurate approximations of phi, the golden ratio, by dividing a number in the series by the one before it.


Why is the Parthenon a Fibonacci sequence?

The limit of Fn/Fn-1 (where Fn is the nth member of the sequence) as n approaches infinity is the golden ratio, approximately 1.62:1. The Parthenon was constructed using this ratio for things like the length to height as it is the ratio at which things appear most attractive to the eye.


A side of math where can you find the golden ratio?

The Fibonacci sequence can be used to determine the golden ratio. If you divide a term in the sequence by its predecessor, at suitably high values, it approaches the golden ratio.

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