namespace summary

{
    internal class Program
    {
        static void Main(string[] args)
        {
            //1. lehetőség
            Console.WriteLine("Give me a natural numner n: ");
            ulong x = ulong.Parse(Console.ReadLine());
            Console.WriteLine("The sum of the first {0} number is: {1} (iterative version)", x, sum1(x));
            Console.WriteLine();
            Console.WriteLine("The sum of the first {0} number is: {1} (rucursive version)", x, sum2(x));
            Console.WriteLine();
            Console.WriteLine("The sum of the first {0} number is: {1} (rucursive version)", x, sum3(1,x));
            Console.WriteLine();
            double y = sum4(x);
            Console.WriteLine("The sum of (1/i^2), where i=1..{0} number is: {1} (rucursive version)", x, y);
            Console.WriteLine();
            Console.WriteLine(Math.Sqrt(6*y));
            Console.ReadLine();
        }

        public static ulong sum1(ulong n)
        {
            ulong s = 0;
            for (ulong i = 1; i < n + 1; i++)
            {
                s += i;
            }
            return s;
        }

        public static ulong sum2(ulong n)
        {
            ulong s;
            if (n == 1)
            {
                s = 1;
            }
            else
            {
                s = n + sum2(n - 1);
            }
            return s;
        }

        public static ulong sum3(ulong n, ulong m)
        {
            ulong s;
            if (n == m)
            {
                s = n;
            }
            else
            {
                ulong k = (n + m) / 2;
                s = sum3(n,k) + sum3(k+1,m);
            }
            return s;
        }

        public static double sum4(ulong n)
        {
            double s;
            if (n == 1)
            {
                s = 1;
            }
            else
            {
                s =  Math.Pow((double) 1 /n,2) + sum4(n - 1);
            }
            return s;
        }
    }
}