# Further Maths - Sums of Natural Numbers

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/sums-of-natural-numbers/ · Updated: 2020-09-14 · Tags: further-maths, series, school

# 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??
$$
\sum^{n}_{r=1} r
$$

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