sum of the first 100 odd numbers
Understand the Problem
The question is asking for the sum of the first 100 odd numbers. To solve it, we will use the formula for the sum of the first n odd numbers, which is nÂ².
Answer
The sum of the first 100 odd numbers is $10000$.
Answer for screen readers
The sum of the first 100 odd numbers is $10000$.
Steps to Solve
- Identify the value of n
In this problem, we need to find the sum of the first 100 odd numbers, so $n = 100$.
- Use the formula for the sum of odd numbers
The formula for the sum of the first $n$ odd numbers is given by:
$$ S_n = n^2 $$
- Substitute the value of n into the formula
Now plug in $n = 100$ into the formula:
$$ S_{100} = 100^2 $$
- Calculate the square of n
Now calculate $100^2$:
$$ S_{100} = 10000 $$
The sum of the first 100 odd numbers is $10000$.
More Information
The result can be illustrated further with a note that the sum of the first ( n ) odd numbers forms a perfect square, showcasing a beautiful aspect of number theory.
Tips
- Confusing the formula for the sum of odd numbers with even numbers. The sum of the first $n$ even numbers is different and follows the formula $n(n + 1)$.
- Forgetting to square the final result after substituting $n$ into the formula.