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Proof binomial theorem by Combination - Binomial Theorem Video Lecture - Class 11
FAQs on Proof binomial theorem by Combination - Binomial Theorem Video Lecture - Class 11
| 1. What is the binomial theorem? |  |
Ans. The binomial theorem is a formula that provides the expansion of a binomial raised to a positive integer power. It states that for any positive integer n, the expansion of (a+b)^n can be expressed as the sum of terms in the form of a^m * b^(n-m), where m ranges from 0 to n.
| 2. How is the binomial theorem proved using combinations? | |
Ans. The binomial theorem can be proved using combinations by considering the coefficients of the expanded terms. The coefficients represent the number of ways to choose the powers of a and b in each term. By using the concept of combinations, it can be shown that these coefficients follow a pattern that aligns with the binomial theorem formula.
| 3. What are combinations in mathematics? | |
Ans. Combinations in mathematics refer to the selection of items from a larger set without considering their order. Combinations are used to count the number of ways in which a subset of items can be chosen from a given set. The number of combinations is denoted by the symbol nCr, where n is the total number of items and r is the number of items to be chosen.
| 4. Why is the binomial theorem important? | |
Ans. The binomial theorem is important as it provides a systematic way to expand binomial expressions without the need for manual multiplication. It enables the simplification of complex expressions and helps in solving problems related to probability, combinatorics, and algebra. The binomial theorem is also widely used in calculus and mathematical analysis.
| 5. Can the binomial theorem be applied to negative exponents? | |
Ans. No, the binomial theorem is applicable only for positive integer exponents. The formula of the binomial theorem is derived specifically for positive integer powers. Attempting to apply the binomial theorem to expressions with negative exponents will not yield valid results. For negative exponents, other mathematical techniques like the concept of negative binomial coefficients need to be employed.
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