What is the 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 this, we can use the formula for the sum of the first n odd numbers, which is n^2. Therefore, we need to calculate 100^2.
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
The formula for the sum of the first $n$ odd numbers is given by $S_n = n^2$.
- Substitute the value of n
In this case, we have $n = 100$. So, we'll substitute this value into the formula: $$ S_{100} = 100^2 $$
- Calculate the square
Now, we need to compute $100^2$: $$ 100^2 = 100 \times 100 $$ which equals $10,000$.
The sum of the first 100 odd numbers is $10,000$.
More Information
The sum of the first $n$ odd numbers can always be found by squaring $n$. This pattern emerges because each odd number increases sequentially by 2, thus forming a perfect square when summed.
Tips
- Confusing the sum formula: A common mistake is using the formula for the sum of all integers or even numbers instead of the odd numbers. Always remember that the sum of the first $n$ odd numbers is $n^2$.
- Incorrect squaring: Sometimes, there’s an error in basic arithmetic when squaring, so double-check your multiplication.
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