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Chapter 8: Mathematical Induction and Binomial Theorem (39 videos)

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
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
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
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. Applications of the Binomial Theorem
3. 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. More on Applications of the Binomial Theorem
3. Problem2-Applications of the Binomial Theorem
 

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