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Pascal's Triangle is a triangle in which each row has one more entry than
the preceding row, each row begins and ends with "1," and the interior elements
are found by adding the adjacent elements in the preceding row. The triangle is
symmetrical.
Figure %: Pascal's Triangle
In Row 6, for example, 15 is the sum of 5 and 10, and 20 is the sum of 10 and
10. Note that the triangle begins with Row 0.
We can find any element of any row using the combination function. The rth element
of Row n is given by:
C(n, r - 1) =
For example, the 3rd entry in Row 6 (r = 3, n = 6) is
C(6, 3 - 1) = C(6, 2) = = 15.
Examples
What is the 5th entry in the Row 7 of Pascal's Triangle? C(7, 4) = = 35.
What is the 6th entry in Row 5 of Pascal's Triangle? C(5, 5) = = 1
What is the 9th entry in Row 20 of Pascal's Triangle? C(20, 8) = = 125970
What is the 2nd entry in Row 103 of Pascal's Triangle? C(103, 1) = = 103
= 15
= 35
= 1
= 125970
= 103
