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Binomial Expansion

Pascal's Triangle

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Problems

Pascal's Triangle

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 r th 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

  1. What is the 5th entry in the Row 7 of Pascal's Triangle?
    C(7, 4) = = 35 .
  2. What is the 6th entry in Row 5 of Pascal's Triangle?
    C(5, 5) = = 1
  3. What is the 9th entry in Row 20 of Pascal's Triangle?
    C(20, 8) = = 125970
  4. What is the 2nd entry in Row 103 of Pascal's Triangle?
    C(103, 1) = = 103

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