The sum of all odd numbers from 1 to 100 is 2500.
To understand this, it's helpful to know what odd numbers are. Odd numbers are whole numbers that cannot be divided evenly by 2. The smallest odd number is 1, as mentioned in the reference. The odd numbers from 1 to 100 are: 1, 3, 5, 7, 9... 99. Instead of adding them one by one, we can utilize a formula to find the sum quickly.
The provided reference states that the sum of all odd numbers from 1 to 100 is 2500. This means that if we add up every odd number from 1 to 99 inclusive, the total will be 2500.
Let's break it down further.
Understanding Odd Numbers
- Odd numbers are not divisible by 2.
- They always end in 1, 3, 5, 7, or 9.
- The first few odd numbers are 1, 3, 5, 7, 9, and so on.
The Sum of First 'n' Odd Numbers
It’s important to note that the question is about all odd numbers till 100, not just the first 'n' odd numbers. However, for reference:
- The sum of the first 'n' odd numbers is given by the formula n2.
- For example, the sum of the first 2 odd numbers (1 and 3) is 22 = 4, the sum of the first 3 odd numbers(1, 3 and 5) is 32=9, and so on.
- However, we don't have "n" here, as we are summing up all odd numbers till a particular value - 100.
Calculating the Sum
The sum of odd numbers from 1 to 100 requires understanding that the largest odd number before 100 is 99. There are 50 odd numbers between 1 and 100. By using the formula where the sum of the first n odd numbers is n2, we might be inclined to think that the sum will be 502 but that is incorrect. The 50th odd number is 99 and the sum of all odd numbers till 99 is indeed equal to 2500.
Summary
Here's a simple summary:
| Category | Details |
|---|---|
| Odd Numbers | Numbers not divisible by 2 |
| Sum of odd numbers from 1 to 100 | 2500 |
