What is the sum of the first 100 odd numbers?
Understand the Problem
The question is asking for the calculation of the sum of the first 100 odd numbers. To solve this, we can use the formula for the sum of the first n odd numbers, which is n^2. In this case, n is 100.
Answer
The sum of the first 100 odd numbers is $10,000$.
Answer for screen readers
The sum of the first 100 odd numbers is $10,000$.
Steps to Solve
- Identify the formula for odd numbers' sum
To calculate the sum of the first $n$ odd numbers, we use the formula:
$$ S_n = n^2 $$
where $S_n$ is the sum and $n$ is the count of odd numbers.
- Substitute the value for n
Here, $n = 100$ since we need the sum of the first 100 odd numbers. Therefore, we substitute $n$ into the formula:
$$ S_{100} = 100^2 $$
- Calculate the result
Now we need to calculate $100^2$:
$$ 100^2 = 100 \times 100 = 10000 $$
So, the sum of the first 100 odd numbers is 10,000.
The sum of the first 100 odd numbers is $10,000$.
More Information
The sum of the first $n$ odd numbers being equal to $n^2$ is a well-known mathematical property. It's fascinating how adding odd numbers systematically leads to perfect squares.
Tips
- Failing to understand the formula: Some might confuse the sum with adding odd numbers directly instead of using the formula.
- Incorrect calculations: Make sure to perform the squaring operation correctly.
