Chapter 8: Mathematical Inductions and Binomial Theorems

 

8.1: Introduction

1. Introduction to Mathematical Induction
2. Problem-Introduction to Mathematical Induction

8.2: Principle of Mathematical Induction

1. Principle of Mathematical Induction
2. More on Principle of Mathematical Induction
3. Problem1-Principle of Mathematical Induction
4. Problem2-Principle of Mathematical Induction
5. Sum of Positive Integral Powers of Natural Numbers

8.3: Principle of Extended Mathematical Induction

1. Principle of Extended Mathematical Induction
2. Problem1-Principle of Extended Mathematical Induction
3. Problem2-Principle of Extended Mathematical Induction

8.4: Binomial Theorem

1. Introduction to Binomial Theorem
2. Problem1-Introduction to Binomial Theorem
3. Problem2-Introduction to Binomial Theorem
4. Proof of Binomial Theorem
5. More on Proof of Binomial Theorem
6. Problem1-Proof of Binomial Theorem
7. Problem2-Proof of Binomial Theorem
8. Deductions From Binomial Theorem
9. Problem1-Deductions From Binomial Theorem
10. Problem2-Deductions From Binomial Theorem
11. Some Important Observations
12. Pascal's Triangle
13. Problem1-Pascal's Triangle
14. Problem2-Pascal's Triangle
15. The Middle Term in the Expansion of ( a + x ) ^2
16. Problem1-The Middle Term in the Binomial Expansion
17. Problem2-The Middle Term in the Binomial Expansion
18. More on Problem2-The Middle Term in the Binomial Expansion
19. Problem3-The Middle Term in the Binomial Expansion
20. Some Deductions From the Binomial Expansion of ( a + x ) ^n
21. Problem1-Some Deductions From the Binomial Expansion
22. Problem2-Some Deductions From the Binomial Expansion
23. Problem3-Some Deductions From the Binomial Expansion

8.5: The Binomial Theorem When the Index n is a Negative Integer or a Fraction

1. The Binomial Theorem When the Index n is a Negative Integer
2. Problem-The Binomial Theorem With Negative Integer Index
3. Some Particular Cases of the Expansion of ( 1 + x ) ^n, n < 0
4. Problem-Some Particular Cases of the Binomial Expansion

8.6: Applications of the Binomial Theorem

1. Applications of the Binomial Theorem
2. More on Applications of the Binomial Theorem
3. Problem1-Applications of the Binomial Theorem
4. Problem2-Applications of the Binomial Theorem