MATHCOUNTS TOOLBOX
Facts, Formulas and Tricks
Lesson 12:
Pascal’s Triangle
&
its uses
Pascal’s Triangle
Pascal’s Triangle Used for Probability
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.
For the Expansion of (a + b)n ,
use numbers in Pascal’s Triangle as coefficients.
For the Expansion of (a + b)n ,
use numbers in Pascal’s Triangle as coefficients.
For 2n, add all the numbers in the nth row.
(Remember the triangle starts with row 0.)
For 2n, add all the numbers in the nth row.
(Remember the triangle starts with row 0.)
Prime Numbers
If the 1st element in a row is a prime number
(remember, the 0th element of every row is 1),
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.
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)
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.
Hockey Stick Pattern
Hockey Stick Pattern
Triangular Numbers
Triangular Numbers
Triangular Numbers
Points on a Circle
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and so on . . .
Fini?