Further Maths - Sums of Natural Numbers

What are the natural numbers?

$1, 2, 3, 4, 5, 6 \dots$

What are the whole numbers?

$0, 1, 2, 3, 4, 5, 6 \dots$

What’s another name for the sum of the first $n$ natural numbers?

The triangle numbers.

How can you visualise the sum of the first $n$ natural numbers?

As a triangle.

How can you visualise the sum of the first $n$ natural numbers, doubled?

As a $n \times (n + 1)$ square.

What are the first 3 triangle numbers?

$1, 3, 6$

What is the formula for the sum of the first $n$ natural numbers?

$\frac{1}{2} n (n + 1)$

What’s the sigma notation for the sum of the first $n$ natural numbers?

\sum_{r = 1}^{n} r

Sums of Natural Numbers