1. PASCAL'S TRIANGLE FOR CLASS XI BENNY VARGHESE P.G.T MATHS J.N.V PUNE
Presented By:
BENNY VARGHESE
P.G.T MATHS
J.N.V PUNE
ROLL NO: GOA_030_005
23 April 2019
By: GOA_030_005

2. 1 2 + 3
OBJECTIVES 1 4 + 5
To acquire the concept of Pascal’s Triangle and to form it
To have the knowledge of various properties of Pascal’s Triangle
To have the knowledge of application side of Pascal’s Triangle
23 April 2019
By: GOA_030_005

3. What’s Pascal’s Triangle
Pascal’s Triangle is the triangular arrangement of coefficients in the expansion of binomials like (a+b)n for n=0,1,2,3,4,5,6,7,…..
Pascal's Triangle is named after Blaise Pascal
23 April 2019
By: GOA_030_005

4. Pascal’s Triangle In Binomial Expansion
(a+b)0 =
(a+b)1 = a + 1b
(a+b)2 = a ab +1b2
(a+b)3 = a a2b +3ab2 +1b3
(a+b)4 = 1a4+ 4ab3+ 6a2b2+ 4ab3+1b4
and so on .
23 April 2019
By: GOA_030_005

5. Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 1 4 6 4 10 5 1 1 5 10
23 April 2019
By: GOA_030_005

6. How To Form Pascal’s Triangle ?
At the tip of Pascal's Triangle is the number 1, which makes up the zeroth row. 1
The first row (1 & 1) contains two 1's, 1 1

7. We may add two cells to get a cell below them
We may add two cells to get a cell below them. Thus 2nd row is : 0+1=1; 1+1=2; 1+0=1. In this way, the rows of the triangle go on infinitely. 2 3 1 +
2nd ROW

8. Pascal’s Triangle From A Practical Situation1

9. Pascal’s Triangle From A Practical Situation

10. Pascal’s Triangle From A Practical Situation

11. Pascal’s Triangle From A Practical Situation

12. Pascal’s Triangle From A Practical Situation

13. Pascal’s Triangle From A Practical Situation

14. Pascal’s Triangle From A Practical Situation

15. Pascal’s Triangle From A Practical Situation

16. Pascal’s Triangle From A Practical Situation

17. Pascal’s Triangle From A Practical Situation

18. Pascal’s Triangle From A Practical Situation

19. Pascal’s Triangle From A Practical Situation

20. Pascal’s Triangle From A Practical Situation

21. Pascal’s Triangle From A Practical Situation

22. Pascal’s Triangle From A Practical Situation

23. Pascal’s Triangle From A Practical Situation

24. Pascal’s Triangle From A Practical Situation1
1 1

25. Row Sum Property Of Pascal’s Triangle1
Sum= 1 = 20 1 1 1
Sum= 2 = 21 1 2 1
Sum= 4 = 22
Sum= 8 = 23 1 3 3
Sum= 16 = 24 1 1 4 6 4 10 5 1
Sum= 32 = 25 1 5 10

26. Hockey Stick Pattern In Pascal’s Triangle
Last number on Hockey stick is the sum of other numbers on it :
= = 13

27. Magic 11’s & Pascal's Triangle
Row 0
Formula
Multidigit Number
Actual row
Row 1
110 1
Row 2
111 11
1 1
Row 3
112
121
1 2 1
Row 4
113
1331
Row 5
114
14641
Row 6
115
161051

28. Fibonacci Sequence From Pascal’s Triangle

29. Triangular Numbers From Pascal's Triangle1 3 6 10

30. QUERY What do you mean by Pascal‘s Triangle ?
Who discovered the importance of all patterns in Pascal’s Triangle ?
Sum of any row of Pascal’s Triangle is the power of ……..
(a) 3 (b) (c) (d) 7
What’s the name of the sequence 1,1,2,3,5,8,…..

31. I’m extremely grateful to :
Hon’ble Dy commissioner, NVS,RO,PUNE
Principal,JNV,Canacona
Principal,JNV,Pune
Mr & Mrs Ekawade, Microsoft