Round #630

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 where the program starts execution. It calls the `CalculateSum` method with the range from 1 to 100 and prints the result. 2. **CalculateSum Method**: This method calculates the sum of integers from a given start value to an end value 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 range (100 in this case). This approach is efficient and leverages a well-known mathematical formula to compute the sum without needing a loop, making it both fast and concise.