Mathematical Induction and Binomial Theorem

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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