Round #620

What is the sum of integers from 1 to 100?

The sum of integers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series: \[ \text{Sum} = \frac{n(n + 1)}{2} \] where \( n \) is the last number in the sequence. For this case, \( n = 100 \). Let's calculate it using C#: ```csharp using System; class Program { static void Main() { int n = 100; int sum = n * (n + 1) / 2; Console.WriteLine("The sum of integers from 1 to 100 is: " + sum); } } ``` When you run this program, it will output: ``` The sum of integers from 1 to 100 is: 5050 ```

To calculate the sum of integers from 1 to 100, you can use a simple loop or take advantage of mathematical formula. Here's how you can do it using C#: ```csharp using System; class Program { static void Main() { int sum = CalculateSum(1, 100); Console.WriteLine($"The sum of integers from 1 to 100 is: {sum}"); } static int CalculateSum(int start, int end) { // Using the formula for the sum of an arithmetic series return (end * (end + 1)) / 2; } } ``` ### Explanation: 1. **Main Method**: This is the entry point of the program where we call the `CalculateSum` method and print the result. 2. **CalculateSum Method**: This method takes two parameters, `start` and `end`, which represent the range of integers to sum. It uses the formula for the sum of an arithmetic series: `(n * (n + 1)) / 2`, where `n` is the last number in the sequence. This approach is efficient because it calculates the sum directly using a mathematical formula, avoiding the need for a loop and thus reducing computational overhead.