Construction
of Pascal's Triangle
The
triangle starts from 1 at the top, which is the 0th row. Numbers are formed
by adding the two numbers above them to the left and the right, all numbers
outside the triangle are considered as 0.
0th row:
1
1st row:
0+1=1, 1+0=1
2nd row:
0+1=1, 1+1=2, 1+0=1
3rd row:
0+1=1, 1+2=3, 2+1=3, 1+0=1
4th row:
0+1=1, 1+3=4, 3+3=6, 3+1=4, 1+0=1
etc.…
In this
way, the rows of the triangle go on infinitely. A number in the triangle
can also be found by nCr (n choose r) where n is the number of the row
and r is the element in that row. The formula for nCr is:
n!
/ r!(n-r)!
!
means factorial, it means proceeding number multiplied by all positive
integers that are smaller than the number.
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