Further Maths - Sums of Natural Numbers
Sums of Natural Numbers
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 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?
\[\sum^{n} _ {r=1} r\]