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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

Lesson 12 dives into Pascal's Triangle, an essential mathematical tool with various applications. It begins with the basics of understanding rows, where row zero contains the first element. Discover how to utilize the triangle for calculating probabilities, such as determining outcomes when flipping coins. Learn about the expansion of (a + b)^n using coefficients from the triangle, and how to find the sum of numbers in any row. The lesson also addresses interesting concepts like prime numbers and the Hockey Stick Pattern, enriching your mathematical knowledge.

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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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  1. MATHCOUNTS TOOLBOXFacts, Formulas and Tricks

  2. Lesson 12: Pascal’s Triangle&its uses

  3. Pascal’s Triangle

  4. Pascal’s Triangle Used for Probability

  5. Remember that the first row is row zero (0). Row 4 is 1 4 6 4 1. This can be used to determine the different outcomes when flipping four coins.

  6. For the Expansion of (a + b)n , use numbers in Pascal’s Triangle as coefficients.

  7. For the Expansion of (a + b)n , use numbers in Pascal’s Triangle as coefficients.

  8. For 2n, add all the numbers in the nth row. (Remember the triangle starts with row 0.)

  9. For 2n, add all the numbers in the nth row. (Remember the triangle starts with row 0.)

  10. Prime Numbers If the 1st element in a row is a prime number (remember, the 0th element of every row is 1),

  11. Prime Numbers If the 1st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it.

  12. Prime Numbers If the 1st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. Example: in row 7 (1 7 21 35 35 21 7 1)

  13. Prime Numbers If the 1st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. Example: in row 7 (1 7 21 35 35 21 7 1), 7, 21, and 35 are all divisible by 7.

  14. Hockey Stick Pattern

  15. Hockey Stick Pattern

  16. Triangular Numbers

  17. Triangular Numbers

  18. Triangular Numbers

  19. Points on a Circle .

  20. Points on a Circle . . .

  21. Points on a Circle . . . . . . . . .

  22. Points on a Circle . . . . . . . . . . . . . . . . . . .

  23. Points on a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  24. Points on a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and so on . . .

  25. Fini?

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