Mathematical Induction and Binomial Theorem

Chapter 8: Mathematical Induction and Binomial Theorem (37 videos)   (Practice Test)

8.1: The Principle of Mathematical Inducion

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

8.2: Sum of Positive Integral Powers of Natural Numbers  (Practice Test)

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
6. Principle of Extended Mathematical Induction
7. Problem1-Principle of Extended Mathematical Induction
8. Problem2-Principle of Extended Mathematical Induction

8.3: Binomial Theorem  (Practice Test)

1. Introduction to Binomial Theorem
2. Problem1-Introduction to Binomial Theorem
3. Problem2-Introduction to Binomial Theorem
4. Pascal's Triangle
5. Problem1-Pascal's Triangle
6. Problem2-Pascal's Triangle

8.4: The Binomial Theorem for a Positive Integral Index  (Practice Test)

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

8.5: Some Important Observations

1. Some Important Observations

8.6: The General Term

1. Deductions From Binomial Theorem
2. Problem1-Deductions From Binomial Theorem
3. Problem2-Deductions From Binomial Theorem

8.7: The Middle Terms

1. The Middle Term in the Expansion of ( a + x ) ^2
2. Problem1-The Middle Term in the Binomial Expansion
3. Problem2-The Middle Term in the Binomial Expansion
4. More on Problem2-The Middle Term in the Binomial Expansion
5. Problem3-The Middle Term in the Binomial Expansion

8.8: The Binomial Series

1. Some Deductions From the Binomial Expansion of ( a + x ) ^n
2. Problem1-Some Deductions From the Binomial Expansion
3. Problem2-Some Deductions From the Binomial Expansion
4. Problem3-Some Deductions From the Binomial Expansion

8.9: Approximations

1. Some Deductions From the Binomial Expansion of ( a + x ) ^n
2. Problem1-Applications of the Binomial Theorem

8.10: Application to Summation of Series

1. Some Deductions From the Binomial Expansion of ( a + x ) ^n
2. Problem2-Applications of the Binomial Theorem