The image shows the formula for the sum of the first $n$ natural numbers:

$1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}$

This is the well-known formula to calculate the sum of an arithmetic series where the first term is 1, the common difference is 1, and the number of terms is $n$. The formula can be derived by recognizing the sequence as an arithmetic progression.

Would you like a step-by-step derivation or an explanation of how this formula works?

Here are five related questions to expand on this:

1. What is the formula for the sum of the first $n$ squares?
2. How can you prove this formula using mathematical induction?
3. Can you derive the sum of the first $n$ odd numbers?
4. How is this formula related to triangular numbers?
5. What is the formula for the sum of the first $n$ terms of a geometric series?

Tip: The sum of the first $n$ terms of an arithmetic series can be calculated even if the sequence does not start at 1; you just need the first term, the last term, and the number of terms!