WHO is PASCAL??
WHAT is his TRIANGLE??
The following are the first few rows of Pascal’s :
1.
Row
Row
Row
Row
Row
Row
0
1
2
3
4
5
1
1
1
5
1
4
1
3
10
1
2
6
1
3
10
1
4
1
5
1
1
By observing the pattern in the above rows, give the next 3 rows of the .
2.
In general, tn,r represents the term in row n, position r.
t 3,0
3.
t 1,1
t 3,2
NOTE: Both the row # and
position # begin at 0.
t 2,2
t 3,3
In general, t n, r = t n-1, r-1 + t n-1, r
t 6,3 = t 5,2 + t 5,3
Use Pascal’s Method to write a formula for each of the following terms:
a) t 12,5
5.
t 3,1
t 2,1
PASCAL’S METHOD:
eg.
4.
t 2,0
t 1,0
t 0,0
b) t 40,32
c) t n+1, r+1
Use Pascal’s Method to express as a single term from Pascal’s :
a) t 5,2 + t 5,3
b) t 21,4 – t 20,4
PASCAL’S TRIANGLE
(Investigation)
Investigation A: ROW SUMS
1.
Fill in the table below as shown in the examples:
ROW
SUM of the TERMS
0
1
2
3
4
5
1
2
EXPRESS as a
BASE of 2
20
21
2.
Predict the sum of the terms in row n.
_____________________
3.
Determine the row that has a sum of 4096.
_____________________
Investigation B: DIVISIBILITY
1.
Determine whether t n,2 is divisible by t n,1 in each row of Pascal’s  by
completing the table below:
Remember…t n,0 is the first term of each row.
ROW
t n,2
t n,1
DIVISIBLE?
0, 1
2
impossible – no t n,2 exists
1
 0.5
2
3
1
3
N/A
3
4
5
6
2.
Describe the observed pattern.
no
yes
Investigation C: TRIANGULAR NUMBERS
1.
Coins can be arranged in the shape of equilateral triangles as shown:
2.
Fill in the table below as shown in the examples:
# of ROWS
# of COINS
1
2
3
4
5
6
1
3
TERM in
PASCAL’S 
t 2,2
t 3,2
3.
Describe the observed pattern.
4.
Relate Pascal’s  to the number of
coins in a triangle with n rows.
_____________________
Predict the number of coins in
a triangle with 12 rows.
_____________________
5.
HOMEWORK:
p.251-252 #1 – 5, 7a, 10