Difference between revisions of "Triangular number"
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For example, the first few triangular numbers can be calculated by adding | For example, the first few triangular numbers can be calculated by adding | ||
1, 1+2, 1+2+3, ... etc. | 1, 1+2, 1+2+3, ... etc. | ||
| − | } | + | <math>} |
rowStart -= 0.5; | rowStart -= 0.5; | ||
} | } | ||
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label( (string) value, (value+5, -2)); | label( (string) value, (value+5, -2)); | ||
} | } | ||
| − | </asy> | + | </asy></math> |
==Formula== | ==Formula== | ||
Revision as of 18:46, 15 July 2020
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.
$}
rowStart -= 0.5;
}
return 0;
}
for (int n=1; n<5; ++n) {
real value= n*(n+1)/2; draw_triangle((value+5,n),n); label( (string) value, (value+5, -2));
} </asy>$ (Error compiling LaTeX. Unknown error_msg)
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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