using System;

using System.Linq;

public class Program

{

        const decimal PI = 3.1415926535897932384626433832m;

        public static void Main(string[] args)

        {

            Console.WriteLine("PI = {0}",PI);

            //Nilakantha Series

            int iterationsN = 100;

            decimal nilakanthaPI = NilakanthaGetPI(iterationsN);

            decimal CalcErrorNilakantha = PI - nilakanthaPI;

            Console.WriteLine("\nNilakantha Series -> PI = {0}",nilakanthaPI);

            Console.WriteLine("Calculation error = {0}",CalcErrorNilakantha);

            int numDecNilakantha = PI.ToString().Zip(nilakanthaPI.ToString(), (x, y) => x == y).TakeWhile(x => x).Count()-2;

            Console.WriteLine("Number of correct decimals = {0}",numDecNilakantha);

            Console.WriteLine("Number of iterations = {0}",iterationsN);

            //Gregory-Leibniz Series

            int iterationsGL = 1000000;

            decimal GregoryLeibnizPI = GregoryLeibnizGetPI(iterationsGL);

            decimal CalcErrorGregoryLeibniz = PI - GregoryLeibnizPI;

            Console.WriteLine("\nGregory-Leibniz Series -> PI = {0}",GregoryLeibnizPI);

            Console.WriteLine("Calculation error = {0}",CalcErrorGregoryLeibniz);

            int numDecGregoryLeibniz = PI.ToString().Zip(GregoryLeibnizPI.ToString(), (x, y) => x == y).TakeWhile(x => x).Count() - 2;

            Console.WriteLine("Number of correct decimals = {0}",numDecGregoryLeibniz);

            Console.WriteLine("Number of iterations = {0}",iterationsGL);

​

            Console.ReadLine();

        }

​

​

        public static decimal GregoryLeibnizGetPI(int n)

        {

            decimal sum = 0;

            decimal temp = 0;

            for (int i = 0; i < n; i++)

            {

                temp = 4m / (1 + 2 * i);

                sum += i % 2 == 0 ? temp : -temp;

            }

            return sum;

        }

        public static decimal NilakanthaGetPI(int n)

        {

            decimal sum = 0;

            decimal temp = 0;

            decimal a = 2, b = 3, c = 4;

            for (int i = 0; i < n; i++)

            {

                temp = 4 / (a * b * c);

                sum += i % 2 == 0 ? temp : -temp;

                a += 2; b += 2; c += 2;

            }

            return 3 + sum;

        }

}