The formula you provided represents a method to compute the 20th Fibonacci number, $F_{20}$, using Binet's formula. This is expressed as:

$F_n = \frac{\phi^n - (1 - \phi)^n}{\sqrt{5}}$

where $\phi$ (the golden ratio) is approximately $1.618034$, and $1 - \phi$ is approximately $-0.618034$. The equation in the image is an approximation for this formula.

The given expression is:

$F_{20} = \frac{(1.618034)^{20} - (0.618034)^{20}}{\sqrt{5}}$

Let me calculate $F_{20}$ for you.The value of $F_{20}$ using the given formula is approximately $6765$, which is the 20th Fibonacci number.

Would you like more details or have any questions about this result?

Here are some related questions you may find interesting:

1. How does Binet's formula approximate Fibonacci numbers?
2. What is the significance of the golden ratio $\phi$ in the Fibonacci sequence?
3. How accurate is this approximation for larger Fibonacci numbers?
4. Can you compute the 21st Fibonacci number using the same formula?
5. What are some real-world applications of the Fibonacci sequence?

Tip: The Fibonacci sequence often appears in nature, such as in the arrangement of leaves or the pattern of a sunflower's seeds!