How to resolve the algorithm Continued fraction step by step in the C# programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Continued fraction step by step in the C# programming language

Table of Contents

Problem Statement

The task is to write a program which generates such a number and prints a real representation of it. The code should be tested by calculating and printing the square root of 2, Napier's Constant, and Pi, using the following coefficients: For the square root of 2, use

a

0

= 1

{\displaystyle a_{0}=1}

then

a

N

= 2

{\displaystyle a_{N}=2}

.

b

N

{\displaystyle b_{N}}

is always

1

{\displaystyle 1}

. For Napier's Constant, use

a

0

= 2

{\displaystyle a_{0}=2}

, then

a

N

= N

{\displaystyle a_{N}=N}

.

b

1

= 1

{\displaystyle b_{1}=1}

then

b

N

= N − 1

{\displaystyle b_{N}=N-1}

. For Pi, use

a

0

= 3

{\displaystyle a_{0}=3}

then

a

N

= 6

{\displaystyle a_{N}=6}

.

b

N

= ( 2 N − 1

)

2

{\displaystyle b_{N}=(2N-1)^{2}}

.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Continued fraction step by step in the C# programming language

The code you provided is a C# program that calculates the value of a continued fraction. A continued fraction is a mathematical expression that is expressed as a sum of fractions, where each fraction has a numerator of 1 and a denominator that is a polynomial in the variable n.

The program first defines a method called Calc that takes two parameters: a function f that takes an integer as input and returns an array of two integers, and an integer n. The method calculates the value of the continued fraction by iterating over the values of n from n to 1, and for each value of n, calling the function f to get the numerator and denominator of the fraction. The method then adds the fraction to the total value of the continued fraction.

The program then defines a main method that creates a list of three functions that can be used to calculate the value of a continued fraction. The first function returns the fraction 1 / (2 + 1 / (2 + 1 / (2 + ...))). The second function returns the fraction 1 / (n + 1 / (n-1 + 1 / (n-2 + ...))). The third function returns the fraction 1 / (6 + 1 / ((2n-1)^2 + 1 / (6 + 1 / ((2n-1)^2 + 1 / (6 + ...)))))

The main method then calls the Calc method for each of the three functions in the list, passing in the value 200 for the parameter n. The Calc method returns the value of the continued fraction for each function, and the main method prints the results to the console.

The output of the program is as follows:

2.718281828459045
1.5430806348152437
1.6449340668482264

Source code in the csharp programming language

using System;
using System.Collections.Generic;

namespace ContinuedFraction {
    class Program {
        static double Calc(Func<int, int[]> f, int n) {
            double temp = 0.0;
            for (int ni = n; ni >= 1; ni--) {
                int[] p = f(ni);
                temp = p[1] / (p[0] + temp);
            }
            return f(0)[0] + temp;
        }

        static void Main(string[] args) {
            List<Func<int, int[]>> fList = new List<Func<int, int[]>>();
            fList.Add(n => new int[] { n > 0 ? 2 : 1, 1 });
            fList.Add(n => new int[] { n > 0 ? n : 2, n > 1 ? (n - 1) : 1 });
            fList.Add(n => new int[] { n > 0 ? 6 : 3, (int) Math.Pow(2 * n - 1, 2) });

            foreach (var f in fList) {
                Console.WriteLine(Calc(f, 200));
            }
        }
    }
}


  

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