Difference between revisions of "Triangular number"
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==Definition== | ==Definition== | ||
− | The <math>n^{th}</math> triangular number is the sum of all natural numbers from one | + | The <math>n^{th}</math> triangular number is the sum of all natural numbers from one ton. |
That is, the <math>n^{th}</math> triangle number is | That is, the <math>n^{th}</math> triangle number is | ||
<math>1 +2+3 + 4............. +(n-1)+(n)</math>. | <math>1 +2+3 + 4............. +(n-1)+(n)</math>. |
Revision as of 10:12, 14 October 2018
The triangular numbers are the numbers which are the sum of the first
natural numbers from
to
.
Definition
The triangular number is the sum of all natural numbers from one ton.
That is, the
triangle number is
.
For example, the first few triangular numbers can be calculated by adding
1, 1+2, 1+2+3, ... etc.
giving the first few triangular numbers to be
.
A rather simple recursive definition can be found by noting that .
They are called triangular because you can make a triangle out of dots, and the number of dots will be a triangular number:
Formula
Using the sum of an arithmetic series formula, a formula can be calculated for :
The formula for finding the triangular number can be written as
.
It can also be expressed as the sum of the row in Pascal's Triangle and all the rows above it. Keep in mind that the triangle starts at Row 0.
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