sum of numbers 1 to 50
Understand the Problem
The question is asking for the sum of all whole numbers from 1 to 50. To solve this, we can use the formula for the sum of an arithmetic series or simply add the numbers sequentially.
Answer
The sum is $1275$.
Answer for screen readers
The sum of all whole numbers from 1 to 50 is $1275$.
Steps to Solve
- Identify the first and last numbers in the series
The first whole number in your series is 1 and the last whole number is 50.
- Use the sum formula for an arithmetic series
The formula for the sum ( S ) of the first ( n ) whole numbers is given by:
$$ S = \frac{n(n + 1)}{2} $$
Here, ( n ) is the last number in the series, which is 50.
- Plug the value into the formula
Substituting ( n = 50 ) into the formula:
$$ S = \frac{50(50 + 1)}{2} $$
- Calculate the sum
Now calculate:
$$ S = \frac{50 \cdot 51}{2} $$
This simplifies to:
$$ S = \frac{2550}{2} $$
- Finalize the answer
So,
$$ S = 1275 $$
The sum of all whole numbers from 1 to 50 is $1275$.
More Information
The formula used, ( S = \frac{n(n + 1)}{2} ), is a well-known shortcut for calculating the sum of the first ( n ) natural numbers and allows for quick calculations without needing to manually add each individual number.
Tips
- Forgetting the division by 2 in the formula, which can lead to doubling the sum.
- Miscalculating ( n(n + 1) ) before dividing, which may result from overlooking the order of operations.