Binomial Theorem JEE Main

What is Binomial Theorem ?

The binomial theorem is a mathematical formula used to expand binomial expressions raised to positive integer exponents. It enables us to calculate the coefficients and terms of the expansion. The theorem finds applications in algebra, combinatorics, and calculus, allowing for simplification of complex expressions and evaluation of binomial coefficients. The coefficients are determined using combinations and follow Pascal's triangle. Understanding the binomial theorem is crucial for solving problems involving binomial expansions, probability calculations, and algebraic manipulations. It provides a valuable tool for simplifying expressions and solving diverse mathematical problems.

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Table of Content 

1. Binomial theorem.

2. Binomial theorem for positive integral index.

3. Some important expansions.

4. General term.

5. Independent term or constant term.

6. Number of terms in the expansion of (a + b + c)n and (a + b + c + d)n.

7. Middle term.

8. To determine a particular term in the expansion.

9. Greatest term and greatest coefficient.

10. Properties of binomial coefficients.

11. An important theorem.

12. Multinomial theorem (For positive integral index) 

13. Binomial theorem for any index.

14. Three/four consecutive terms or coefficients.

15. Some important points.

16. First principle of mathematical induction.