1 + 2 + 3 + ... + 30
Understand the Problem
The question is asking for the sum of a series of consecutive integers starting from 1 and ending at 30. This can be solved using the formula for the sum of the first n natural numbers.
Answer
The sum is $465$.
Answer for screen readers
The sum of the integers from 1 to 30 is 465, represented as:
$$ S = 465 $$
Steps to Solve
- Identify the end number
We are summing integers from 1 to 30, so our end number, $n$, is 30.
- Use the formula for the sum of the first n natural numbers
The formula for the sum $S$ of the first $n$ natural numbers is given by:
$$ S = \frac{n(n + 1)}{2} $$
- Substitute the value of n into the formula
Substituting $n = 30$ into the formula:
$$ S = \frac{30(30 + 1)}{2} $$
This simplifies to:
$$ S = \frac{30 \times 31}{2} $$
- Calculate the sum
Now compute the product and then divide:
$$ S = \frac{930}{2} = 465 $$
The sum of the integers from 1 to 30 is 465, represented as:
$$ S = 465 $$
More Information
The formula for the sum of the first $n$ natural numbers is a well-known result in mathematics and is a quick way to calculate the sum of a series of consecutive integers without adding each one individually.
Tips
- Forgetting to correctly apply the formula can lead to errors. Always ensure to substitute the right value for $n$.
- Miscalculating $n(n + 1)$ can happen; double-check your multiplication before dividing.
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