AoPS_CP Week 12: Pascal’s Triangle

lilijia Post in AOPS_Counting_Probability，
08 December 2019
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AoPS_CP Week 12: Pascal’s Triangle

Lesson Review:

Pascal’s Triangle (also known as Yanghui Triangle in China) is a triangular array constructed by summing adjacent elements in preceding rows. It is widely used in counting and polynomial expressions.

The entries of Pascal’s Triangle are the combinations (n choose r).

The numbers of Pascal’s Triangle also count the number of paths from the top of the triangle to the point where the number appears.

The sum of each row in Pascal’s Triangle = 2^n.

Pascal’s Identity:

Homework:

  • P180 Ex 12.3.1, 12.3.3
  • P184 Ex 12.4.1 (a)
  • P186 Ex 12.5.1
  • P187 Ex 12.12
  • P189 Ex 12.19, 12.20

Other Resources:

https://artofproblemsolving.com/wiki/index.php/Pascal%27s_triangle

https://www.mathsisfun.com/pascals-triangle.html

https://medium.com/i-math/top-10-secrets-of-pascals-triangle-6012ba9c5e23

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:polynomials/x9e81a4f98389efdf:binomial/v/pascals-triangle-binomial-theorem

https://artofproblemsolving.com/wiki/index.php/Pascal%27s_Identity

Something Else:

*I will be back to China from 12/10 to 12/27. Next Sunday (12/15) we will have Mr. Xu (the teacher of AoPS: Precalculus) to teach Ch.11 Expected Value and Ch. 13 The Hockey Stick Identity. Thank you, Mr. Xu!

There is no school on 12/22 and 12/29. Merry Christmas and Happy New Year, everyone! See you on 1/5/2020 for our last class before the final exam on 1/12!

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