Problem 6

The sum of the squares of the first ten natural numbers is,

1² + 2² + … + 10² = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Solution

//The sum of the squares of

 //the first ten natural numbers is,

 

 //1^2 + 2^2 + … + 10^2 = 385

 //The square of the sum of the

 //first ten natural numbers is,

 

 //(1 + 2 + … + 10)^2 = 55^2 = 3025

 //Hence the difference between the sum

 //of the squares of the first ten natural

 //numbers and the square of the sum is

 //3025 – 385 = 2640.

 

 //Find the difference between the sum of

 //the squares of the first one hundred natural

 //numbers and the square of the sum.

 

 

namespace ProjectEulerCSharp_006

{

    class Program

    {

        static void Main(string[] args)

        {

            int sumsqrs = 0;

            int sqrsums = 0;

            for (int i = 0; i <= 100; i++)

            {

                sumsqrs += i * i;

                sqrsums += i;

            }

            sqrsums *= sqrsums;

            System.Console.WriteLine(sqrsums – sumsqrs);

        }

    }

}

 

Discussion

No trick today. 

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).