<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["en", "en"].<end_of_turn>
<start_of_turn>user
What is the Fibonacci sequence?<end_of_turn>
<start_of_turn>model
The Fibonacci sequence is a sequence in which we start with 0 and 1, and then each new number is the sum of the last two numbers we have. For example, the first 10 terms of the sequence would be: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. We can see that 1=0+1, 2=1+1, 3=2 +1, 5=3+2, 8=5+3, 13=8+5, 21=13+8, 32=21+12. So the next number would be 34+21=55.
Mathematically, we can say that this is a second-order linear recurrence f(n), where f(n) is the nth number in the sequence.
Obviously, f(n) = f(n-1) + f(n-2) for any n > 1, and f(0) = 0, f(1) = 1.

There is a closed (non-recurring) formula to calculate f(n). Is the next:
f(n) = ((1+sqrt(5))^n - (1-sqrt(5))^n)/(sqrt(5)*2^n)<end_of_turn><eos>