What is the sum of the first ten natural numbers?

To determine the sum of the first ten natural numbers, we can use the formula for the sum of an arithmetic series. The first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The formula for the sum ( S ) of the first ( n ) natural numbers is given by:

[

S = \frac{n(n + 1)}{2}

]

In this case, ( n = 10 ). Plugging that value into the formula:

[

S = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} = \frac{110}{2} = 55

]

Thus, the sum of the first ten natural numbers is 55. This approach effectively confirms the calculated total using a systematic method for summation.

This demonstrates the power of mathematical formulas for efficiently solving problems rather than relying solely on repeated addition, which can be prone to errors, especially as the number of addends increases.