# Triangular number

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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