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The Fibonacci sequence is a simple numerical pattern that starts with 1 and 1, where each new number is obtained by adding the two previous ones. This rule produces a sequence that grows steadily and predictably, yet it has deep significance across many areas of mathematics, including number theory, recursion, and algorithms. One of the most striking features of the sequence is how the ratio of consecutive terms gradually settles toward a constant value known as the golden ratio. This limiting b
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