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 to <math>n</math>. |
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>. | ||
| Line 21: | Line 21: | ||
} | } | ||
</asy> | </asy> | ||
| + | |||
==Formula== | ==Formula== | ||
Revision as of 22:41, 21 February 2019
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 to .
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.
} rowStart -= 0.5; } return 0;
}
for (int n=1; n<5; ++n) {
real value= n*(n+1)/2; draw_triangle((value+5,n),n); label( (string) value, (value+5, -2));
} </asy>
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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