Further Maths - Sums of Natural Numbers
Sums of Natural Numbers
What are the natural numbers?
$1, 2, 3, 4, 5, 6\ldots$
What are the whole numbers?
$0, 1, 2, 3, 4, 5, 6\ldots$
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?
\[\sum^{n}_{r=1} r\]