Pascal's Triangle
Speaking of Pascal's triangle, it can be characterized as an infinite table. This table uses binomial coefficients. The table itself is presented in the form of a triangle. To perform calculations, you can use a calculator where only the number of rows is specified. Manual calculation requires time and knowledge of formulas.
As already mentioned, this triangle is a table that starts with the zeroth row. The top of the table and the side edges of each row have ones. The remaining numbers (in the middle) are equal to the sum of the 2 numbers located in the previous row (above them).
In this case, natural powers of the binomial are used:
x+at
For the zeroth row:
(x + y)° =
For the first:
(x + y)¹ =
For the second:
(x + y)² =
And so on.
If you decompose into the sum of monomials, you get for the zeroth: 1
For the first:
1x + 1y
For the second:
1x² + 2xy + 1y²
Pascal's triangle, for calculations, uses the formula:
where
