SlideShare uma empresa Scribd logo
1 de 33
Binomial Theorem
Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1
Blaise Pascal saw a pattern which we now know as  Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1
 
 
 
 
 
 
 
 
 
 
 
 
 
Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23

Mais conteúdo relacionado

Destaque

Binomial Theorem
Binomial TheoremBinomial Theorem
Binomial Theoremitutor
 
Binomial theorem for any index
Binomial theorem for any indexBinomial theorem for any index
Binomial theorem for any indexindu psthakur
 
12 x1 t08 02 general binomial expansions (2012)
12 x1 t08 02 general binomial expansions (2012)12 x1 t08 02 general binomial expansions (2012)
12 x1 t08 02 general binomial expansions (2012)Nigel Simmons
 
CIS Anaesthesia Software
CIS Anaesthesia SoftwareCIS Anaesthesia Software
CIS Anaesthesia Softwaresteensgaard
 
6.4 binomials containing radicals
6.4 binomials containing radicals6.4 binomials containing radicals
6.4 binomials containing radicalsandreagoings
 
The binomial theorem
The binomial theoremThe binomial theorem
The binomial theoremMaxTorresdey
 
119 Powerpoint 1.6
119 Powerpoint 1.6119 Powerpoint 1.6
119 Powerpoint 1.6Jeneva Clark
 
L10 binomial theorem
L10 binomial theoremL10 binomial theorem
L10 binomial theoremisaiah777
 
Sequences, Series, and the Binomial Theorem
Sequences, Series, and the Binomial TheoremSequences, Series, and the Binomial Theorem
Sequences, Series, and the Binomial TheoremVer Louie Gautani
 
Sequence and series
Sequence and seriesSequence and series
Sequence and seriesviannafaye
 
6 binomial theorem
6 binomial theorem6 binomial theorem
6 binomial theoremmath123c
 
Sequence powerpoint
Sequence powerpointSequence powerpoint
Sequence powerpointcomlabfolder
 
Multiplying binomials
Multiplying binomialsMultiplying binomials
Multiplying binomialsEDS
 
13 sequences and series
13   sequences and series13   sequences and series
13 sequences and seriesKathManarang
 

Destaque (20)

Binomial Theorem
Binomial TheoremBinomial Theorem
Binomial Theorem
 
Binomial theorem for any index
Binomial theorem for any indexBinomial theorem for any index
Binomial theorem for any index
 
12 x1 t08 02 general binomial expansions (2012)
12 x1 t08 02 general binomial expansions (2012)12 x1 t08 02 general binomial expansions (2012)
12 x1 t08 02 general binomial expansions (2012)
 
CIS Anaesthesia Software
CIS Anaesthesia SoftwareCIS Anaesthesia Software
CIS Anaesthesia Software
 
6.4 binomials containing radicals
6.4 binomials containing radicals6.4 binomials containing radicals
6.4 binomials containing radicals
 
1114 ch 11 day 14
1114 ch 11 day 141114 ch 11 day 14
1114 ch 11 day 14
 
The binomial theorem
The binomial theoremThe binomial theorem
The binomial theorem
 
Matlab II
Matlab IIMatlab II
Matlab II
 
119 Powerpoint 1.6
119 Powerpoint 1.6119 Powerpoint 1.6
119 Powerpoint 1.6
 
L10 binomial theorem
L10 binomial theoremL10 binomial theorem
L10 binomial theorem
 
Binomial
BinomialBinomial
Binomial
 
Polynomials
Polynomials Polynomials
Polynomials
 
Sequences, Series, and the Binomial Theorem
Sequences, Series, and the Binomial TheoremSequences, Series, and the Binomial Theorem
Sequences, Series, and the Binomial Theorem
 
Binomial theorem
Binomial theoremBinomial theorem
Binomial theorem
 
Sequence and series
Sequence and seriesSequence and series
Sequence and series
 
Polynomials
PolynomialsPolynomials
Polynomials
 
6 binomial theorem
6 binomial theorem6 binomial theorem
6 binomial theorem
 
Sequence powerpoint
Sequence powerpointSequence powerpoint
Sequence powerpoint
 
Multiplying binomials
Multiplying binomialsMultiplying binomials
Multiplying binomials
 
13 sequences and series
13   sequences and series13   sequences and series
13 sequences and series
 

Mais de Nigel Simmons

Goodbye slideshare UPDATE
Goodbye slideshare UPDATEGoodbye slideshare UPDATE
Goodbye slideshare UPDATENigel Simmons
 
12 x1 t02 02 integrating exponentials (2014)
12 x1 t02 02 integrating exponentials (2014)12 x1 t02 02 integrating exponentials (2014)
12 x1 t02 02 integrating exponentials (2014)Nigel Simmons
 
11 x1 t01 03 factorising (2014)
11 x1 t01 03 factorising (2014)11 x1 t01 03 factorising (2014)
11 x1 t01 03 factorising (2014)Nigel Simmons
 
11 x1 t01 02 binomial products (2014)
11 x1 t01 02 binomial products (2014)11 x1 t01 02 binomial products (2014)
11 x1 t01 02 binomial products (2014)Nigel Simmons
 
12 x1 t02 01 differentiating exponentials (2014)
12 x1 t02 01 differentiating exponentials (2014)12 x1 t02 01 differentiating exponentials (2014)
12 x1 t02 01 differentiating exponentials (2014)Nigel Simmons
 
11 x1 t01 01 algebra & indices (2014)
11 x1 t01 01 algebra & indices (2014)11 x1 t01 01 algebra & indices (2014)
11 x1 t01 01 algebra & indices (2014)Nigel Simmons
 
12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)Nigel Simmons
 
12 x1 t01 02 differentiating logs (2013)
12 x1 t01 02 differentiating logs (2013)12 x1 t01 02 differentiating logs (2013)
12 x1 t01 02 differentiating logs (2013)Nigel Simmons
 
12 x1 t01 01 log laws (2013)
12 x1 t01 01 log laws (2013)12 x1 t01 01 log laws (2013)
12 x1 t01 01 log laws (2013)Nigel Simmons
 
X2 t02 04 forming polynomials (2013)
X2 t02 04 forming polynomials (2013)X2 t02 04 forming polynomials (2013)
X2 t02 04 forming polynomials (2013)Nigel Simmons
 
X2 t02 03 roots & coefficients (2013)
X2 t02 03 roots & coefficients (2013)X2 t02 03 roots & coefficients (2013)
X2 t02 03 roots & coefficients (2013)Nigel Simmons
 
X2 t02 02 multiple roots (2013)
X2 t02 02 multiple roots (2013)X2 t02 02 multiple roots (2013)
X2 t02 02 multiple roots (2013)Nigel Simmons
 
X2 t02 01 factorising complex expressions (2013)
X2 t02 01 factorising complex expressions (2013)X2 t02 01 factorising complex expressions (2013)
X2 t02 01 factorising complex expressions (2013)Nigel Simmons
 
11 x1 t16 07 approximations (2013)
11 x1 t16 07 approximations (2013)11 x1 t16 07 approximations (2013)
11 x1 t16 07 approximations (2013)Nigel Simmons
 
11 x1 t16 06 derivative times function (2013)
11 x1 t16 06 derivative times function (2013)11 x1 t16 06 derivative times function (2013)
11 x1 t16 06 derivative times function (2013)Nigel Simmons
 
11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)Nigel Simmons
 
11 x1 t16 04 areas (2013)
11 x1 t16 04 areas (2013)11 x1 t16 04 areas (2013)
11 x1 t16 04 areas (2013)Nigel Simmons
 
11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)Nigel Simmons
 
11 x1 t16 02 definite integral (2013)
11 x1 t16 02 definite integral (2013)11 x1 t16 02 definite integral (2013)
11 x1 t16 02 definite integral (2013)Nigel Simmons
 

Mais de Nigel Simmons (20)

Goodbye slideshare UPDATE
Goodbye slideshare UPDATEGoodbye slideshare UPDATE
Goodbye slideshare UPDATE
 
Goodbye slideshare
Goodbye slideshareGoodbye slideshare
Goodbye slideshare
 
12 x1 t02 02 integrating exponentials (2014)
12 x1 t02 02 integrating exponentials (2014)12 x1 t02 02 integrating exponentials (2014)
12 x1 t02 02 integrating exponentials (2014)
 
11 x1 t01 03 factorising (2014)
11 x1 t01 03 factorising (2014)11 x1 t01 03 factorising (2014)
11 x1 t01 03 factorising (2014)
 
11 x1 t01 02 binomial products (2014)
11 x1 t01 02 binomial products (2014)11 x1 t01 02 binomial products (2014)
11 x1 t01 02 binomial products (2014)
 
12 x1 t02 01 differentiating exponentials (2014)
12 x1 t02 01 differentiating exponentials (2014)12 x1 t02 01 differentiating exponentials (2014)
12 x1 t02 01 differentiating exponentials (2014)
 
11 x1 t01 01 algebra & indices (2014)
11 x1 t01 01 algebra & indices (2014)11 x1 t01 01 algebra & indices (2014)
11 x1 t01 01 algebra & indices (2014)
 
12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)12 x1 t01 03 integrating derivative on function (2013)
12 x1 t01 03 integrating derivative on function (2013)
 
12 x1 t01 02 differentiating logs (2013)
12 x1 t01 02 differentiating logs (2013)12 x1 t01 02 differentiating logs (2013)
12 x1 t01 02 differentiating logs (2013)
 
12 x1 t01 01 log laws (2013)
12 x1 t01 01 log laws (2013)12 x1 t01 01 log laws (2013)
12 x1 t01 01 log laws (2013)
 
X2 t02 04 forming polynomials (2013)
X2 t02 04 forming polynomials (2013)X2 t02 04 forming polynomials (2013)
X2 t02 04 forming polynomials (2013)
 
X2 t02 03 roots & coefficients (2013)
X2 t02 03 roots & coefficients (2013)X2 t02 03 roots & coefficients (2013)
X2 t02 03 roots & coefficients (2013)
 
X2 t02 02 multiple roots (2013)
X2 t02 02 multiple roots (2013)X2 t02 02 multiple roots (2013)
X2 t02 02 multiple roots (2013)
 
X2 t02 01 factorising complex expressions (2013)
X2 t02 01 factorising complex expressions (2013)X2 t02 01 factorising complex expressions (2013)
X2 t02 01 factorising complex expressions (2013)
 
11 x1 t16 07 approximations (2013)
11 x1 t16 07 approximations (2013)11 x1 t16 07 approximations (2013)
11 x1 t16 07 approximations (2013)
 
11 x1 t16 06 derivative times function (2013)
11 x1 t16 06 derivative times function (2013)11 x1 t16 06 derivative times function (2013)
11 x1 t16 06 derivative times function (2013)
 
11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)
 
11 x1 t16 04 areas (2013)
11 x1 t16 04 areas (2013)11 x1 t16 04 areas (2013)
11 x1 t16 04 areas (2013)
 
11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)
 
11 x1 t16 02 definite integral (2013)
11 x1 t16 02 definite integral (2013)11 x1 t16 02 definite integral (2013)
11 x1 t16 02 definite integral (2013)
 

Último

Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17  How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17  How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin ClassesCeline George
 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701bronxfugly43
 
Fostering Friendships - Enhancing Social Bonds in the Classroom
Fostering Friendships - Enhancing Social Bonds  in the ClassroomFostering Friendships - Enhancing Social Bonds  in the Classroom
Fostering Friendships - Enhancing Social Bonds in the ClassroomPooky Knightsmith
 
How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17Celine George
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and ModificationsMJDuyan
 
SOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning PresentationSOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning Presentationcamerronhm
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfSherif Taha
 
Google Gemini An AI Revolution in Education.pptx
Google Gemini An AI Revolution in Education.pptxGoogle Gemini An AI Revolution in Education.pptx
Google Gemini An AI Revolution in Education.pptxDr. Sarita Anand
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxheathfieldcps1
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsMebane Rash
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxVishalSingh1417
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSCeline George
 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxAreebaZafar22
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxVishalSingh1417
 
Micro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdfMicro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdfPoh-Sun Goh
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Association for Project Management
 
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...ZurliaSoop
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.MaryamAhmad92
 

Último (20)

Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17  How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17  How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
 
Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024
 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
 
Fostering Friendships - Enhancing Social Bonds in the Classroom
Fostering Friendships - Enhancing Social Bonds  in the ClassroomFostering Friendships - Enhancing Social Bonds  in the Classroom
Fostering Friendships - Enhancing Social Bonds in the Classroom
 
How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17
 
Understanding Accommodations and Modifications
Understanding  Accommodations and ModificationsUnderstanding  Accommodations and Modifications
Understanding Accommodations and Modifications
 
SOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning PresentationSOC 101 Demonstration of Learning Presentation
SOC 101 Demonstration of Learning Presentation
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdf
 
Google Gemini An AI Revolution in Education.pptx
Google Gemini An AI Revolution in Education.pptxGoogle Gemini An AI Revolution in Education.pptx
Google Gemini An AI Revolution in Education.pptx
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptx
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptx
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
 
ICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptxICT Role in 21st Century Education & its Challenges.pptx
ICT Role in 21st Century Education & its Challenges.pptx
 
Spatium Project Simulation student brief
Spatium Project Simulation student briefSpatium Project Simulation student brief
Spatium Project Simulation student brief
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
 
Micro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdfMicro-Scholarship, What it is, How can it help me.pdf
Micro-Scholarship, What it is, How can it help me.pdf
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...
 
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.
 

12X1 T08 01 binomial expansions

  • 2. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 3. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 4. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 5. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 6. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 7. Binomial Theorem Binomial Expansions A binomial expression is one which contains two terms.
  • 8. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle
  • 9. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1
  • 10. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1
  • 11. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1
  • 12. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1
  • 13. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1
  • 14. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
  • 15. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1
  • 16. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1
  • 17. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1
  • 18. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1
  • 19. Blaise Pascal saw a pattern which we now know as Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1
  • 20.  
  • 21.  
  • 22.  
  • 23.  
  • 24.  
  • 25.  
  • 26.  
  • 27.  
  • 28.  
  • 29.  
  • 30.  
  • 31.  
  • 32.  
  • 33. Exercise 5A; 2ace etc, 4, 6, 7, 9ad, 12b, 13ac, 14ace, 16a, 22, 23