How to Add Odd Numbers from 1 to 100?

The sum of odd numbers from 1 to 100 is 2500.

Understanding the Problem

This question is asking for the total sum when you add all the odd numbers starting from 1 up to and including 100. These are numbers like 1, 3, 5, 7, and so on. There's a simple method to calculate this without manually adding each number.

The Formula

The key is to understand a mathematical property: The sum of the first n odd numbers is equal to n².

• n represents the number of odd numbers we are adding.
• n² is n multiplied by itself.

Calculating the Sum

1. Identify n: There are 50 odd numbers from 1 to 100 (1, 3, 5,... 99). So, n = 50.

2. Apply the Formula: The sum of the odd numbers from 1 to 100 equals n², which is 50²

3. Solve: 50² = 50 * 50 = 2500

Example Calculation Table

Odd Numbers from 1 to 100	Number of Odd Numbers (n)	Sum (n2)
1,3,5...99	50	2500

Conclusion

Therefore, the sum of all odd numbers from 1 to 100 is 2500. This is based on the mathematical property that the sum of the first 'n' odd numbers equals n squared.