The sum of the first 10 positive integers \(1 + 2 + 3 + \dots + 10\) can be calculated using the formula for the sum of an arithmetic series:

\[
S_n = \frac{n}{2} \times (a_1 + a_n)
\]

Where:
- \(n\) is the number of terms,
- \(a_1\) is the first term,
- \(a_n\) is the last term.

For this series:
- \(n = 10\),
- \(a_1 = 1\),
- \(a_n = 10\).

Now, plug in the values:

\[
S_{10} = \frac{10}{2} \times (1 + 10) = 5 \times 11 = 55
\]

So, the sum \(1 + 2 + 3 + \dots + 10 = 55\).

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:
1. What is the sum of the first 20 positive integers?
2. How do you find the sum of the first \(n\) odd numbers?
3. What is the sum of the first 10 even numbers?
4. How do you find the sum of the first \(n\) squares?
5. Can you prove the formula for the sum of an arithmetic series?

**Tip:** The sum of the first \(n\) positive integers is also given by the formula \( \frac{n(n + 1)}{2} \).

Discover how to find the sum of the first 10 positive integers (1+2+3+...+10) using the arithmetic series formula. This problem highlights key concepts in arithmetic series and summation, ideal for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation