Binet's formula provides an explicit expression for the \(n\)th Fibonacci number \(F_n\) using the golden ratio. The formula is:

\[
F_n = \frac{1}{\sqrt{5}} \left( \varphi^n - \psi^n \right)
\]

where:
- \(\varphi = \frac

Explore Binet's formula, an explicit expression for the nth Fibonacci number using the golden ratio. This formula provides insights into recursive sequences and mathematical constants, suitable for advanced high school and college-level students.

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