Question

Надо записать в c# две формулы для чисел Фибоначчи uk=(1/5)1/2((1+51/2)/2)k И uk=uk-1+uk-2

Answer 1

Ответ:

           double uk = (1/5)*(1/2)*((1+51/2)/2)*k;

           uk = uk-1+uk-2;

Объяснение:

Answer 2

To calculate the nth Fibonacci number using the given formulas, you can create a C# program that implements both formulas. The first formula is an explicit formula for the nth Fibonacci number, and the second formula is a recursive relation. Here's how you can do it:

1. Using the explicit formula:

csharpCopy code
using System;

class Fibonacci
{
    // Function to calculate the nth Fibonacci number using the explicit formula
    static double FibonacciExplicit(int n)
    {
        double sqrt5 = Math.Sqrt(5);
        double phi1 = (1 + sqrt5) / 2;
        double phi2 = (1 - sqrt5) / 2;
        double nthFibonacci = (Math.Pow(phi1, n) - Math.Pow(phi2, n)) / sqrt5;
        return nthFibonacci;
    }

    static void Main()
    {
        Console.Write("Enter the value of n to calculate the nth Fibonacci number: ");
        int n = int.Parse(Console.ReadLine());

        double result = FibonacciExplicit(n);
        Console.WriteLine($"The {n}th Fibonacci number is: {result}");
    }
}

2. Using the recursive relation:

csharpCopy code
using System;

class Fibonacci
{
    // Function to calculate the nth Fibonacci number using the recursive relation
    static double FibonacciRecursive(int n)
    {
        if (n <= 0)
            return 0;
        else if (n == 1)
            return 1;
        else
            return FibonacciRecursive(n - 1) + FibonacciRecursive(n - 2);
    }

    static void Main()
    {
        Console.Write("Enter the value of n to calculate the nth Fibonacci number: ");
        int n = int.Parse(Console.ReadLine());

        double result = FibonacciRecursive(n);
        Console.WriteLine($"The {n}th Fibonacci number is: {result}");
    }
}

Please note that the recursive approach (second formula) may not be efficient for large values of n as it recalculates Fibonacci numbers multiple times. You might encounter performance issues for larger values of n. In such cases, it's better to use more efficient algorithms like memoization or iterative approaches for calculating Fibonacci numbers.