1.4 Pascal’s Triangle

**Test Sept. 25/26**

Pascal’s Triangle is an array of numbers with a few rules:

Rule #1 We do not talk about Pascal’s Triangle.

Rule #2 We do not talk about Pascal’s Triangle.

Seriously,

1. Always begin counting the rows and columns at 0.

2. Always begin and end each row with 1.

3. There is always one more number in the next row.

4. Each number is equal to the two numbers directly above it.

Write out Pascal’s Triangle from rows 0 to 6.

Patterns in Pascal’s Triangle

Ex 1 (a) Calculate the sum of the rows for rows 0-4 of Pascal’s Triangle.

(b) What is the sum of the 10^th, 12^th, 16^th rows?

Ex 2 The first 6 terms in row 25 of Pascal’s Triangle are 1, 25, 300, 2300, 12650, 53130.

(a) Determine the first 6 terms in row 26

(b) Write a formula for: , ,

What does equal-in terms of other n, r?

Ex 3 Triangular Numbers are numbers in the following pattern: 1, 3, 6, 10 – where each number is the equal to the sum of the first n natural numbers-for example

(a) Write a list of the first six triangular numbers.

(b) Find these numbers on Pascal’s Triangle.

(c) Which term in Pascal’s Triangle will tell you how many items there are in a triangle with 12 rows?

Ex 4 Can you find a relationship between perfect squares and the sums of pairs of entries in Pascal’s Triangle?

p. 251#2-7, 10-13