Difference between revisions of "Triangular number"
(→Definition) |
Sakshamsethi (talk | contribs) (→Definition) |
||
| Line 8: | Line 8: | ||
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; | ||
} | } | ||
| Line 20: | Line 20: | ||
label( (string) value, (value+5, -2)); | label( (string) value, (value+5, -2)); | ||
} | } | ||
| − | </asy> | + | </asy></math> |
==Formula== | ==Formula== | ||
Revision as of 19:46, 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.
This article is a stub. Help us out by expanding it.
