The ordered arrangement of binomial numbers, as in the table below, is called Pascal's Triangle.
In this triangular table, binomial numbers with the same numerator are written on the same row and those of the same denominator in the same column.
For example, binomial numbers , , and are on line 3 and the binomial numbers , , , ,… , ,… Are in column 1.
Replacing each binomial number with its value, we have:
Pascal Triangle Construction
To construct the Pascal triangle, just remember the following properties of binomial numbers, not having to calculate them:
1st) How = 1, all elements in column 0 are equal to 1.
2nd) How = 1, the last element of each line is equal to 1.
3ª) Each element of the triangle that is not from column 0 nor the last of each row is equal to the sum of the one that is in the same column and previous row with the element to the left of the latter (Stifel relation).
Observe the steps and application of the Stifel relation for the triangle construction:
Next: Pascal Triangle Properties