Pascals Triangle

1
Pascals Triangle
2
1
3
1
1
1
4
1
1
1

2
5
1
1
1
2
1
1
6
1
1
1
2
1
1

3
7
1
1
1
2
1
1

3
3
8
1
1
1
2
1
1
3
3
1
1
9
1
1
1
2
1
1
3
3
1
1
4
10
1
1
1
2
1
1
3
3
1
1
4
4
11
1
1
1
2
1
1
3
3
1
1
4
4
6
12
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
13
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
14
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
15
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
16
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
17
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
18
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
19
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
20
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
21
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
22
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
23
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
24
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1

This pattern continues forever.
25
Pascals Triangle is filled with patterns.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1

26
Increasing by one.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1

27
Increasing by 2, then 3, then 4, then 5.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1

28
Increasing by 3, then 6, then 10, then 15.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1

29
Pascals Triangle also has symmetry.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1

30
Some patterns are not very obvious.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
31
Some patterns are not very obvious.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
32
Calculate the sum of each row.
1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
33
Calculate the sum of each row.
1
1
ROW 1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
34
Calculate the sum of each row.
1
1
ROW 1
1
1
ROW 2

2
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
35
Calculate the sum of each row.
1
1
ROW 1
1
1
ROW 2

2
2
1
1
ROW 3
4


3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
36
Calculate the sum of each row.
1
ROW 1
1
1
1
ROW 2

2
2
1
1
ROW 3
4


8
3
3
1
1
ROW 4



4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
37
Calculate the sum of each row.
1
ROW 1
1
1
1
ROW 2

2
2
1
1
ROW 3
4


8
3
3
1
1
ROW 4



4
4
6
1
1
ROW 5
16




5
5
10
10
1
1
6
6
15
15
20
1
1
38
Lets chart our findings.
1
ROW 1
1
1
1
ROW 2

2
2
1
1
ROW 3
4


8
3
3
1
1
ROW 4



4
4
6
1
1
ROW 5
16




5
5
10
10
1
1
ROW 6
32





6
6
15
15
20
1
1
39
Lets chart our findings.
40
The sum of a particular row is double the sum of
the previous row.
X 2
41
Each sum can be written as the product of twos.
42
Each sum can be written as the product of twos.
43
Expressions that multiply the same number over
and over again can be written using exponents.
44
Expressions that multiply the same number over
and over again can be written using exponents.
45
Expressions that multiply the same number over
and over again can be written using exponents.
46
Expressions that multiply the same number over
and over again can be written using exponents.
47
Expressions that multiply the same number over
and over again can be written using exponents.
48
Expressions that multiply the same number over
and over again can be written using exponents.
49
What is the exponential expression that equals 1 ?
50
What is the exponential expression that equals 1 ?
51
What is the exponential expression that equals 1 ?
Any base raised to the power of zero is always 1.
52
Check out this cool website for more patterns
within Pascals Triangle.http//www.shodor.org/in
teractivate/activities/pascal1/index.html
53
THE END!