Using Binomial theorem to prove statements | Binomial Theorem | Grade 11 | Math | Khan Academy

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In this video, we apply binomial theorem to prove statements on divisibility. In such problems, we're given an expression and a statement that is true for all values of n. Our task is to strategically expand a binomial such that the expansion gives terms that match the given statement. We first prove that a given expression is always divisible by 64. We then prove that a given expression always leaves remainder 1 when divided by 25. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:binomial-theorem-ncert-new/xea4762213f311c5e:binomial-theorem-for-positive-integral-indices/e/binomial-theorem) Timestamps: 00:00 Proving that a given expression is always divisible by 64. 01:12 Strategy to solve such problems - writing down the clues 02:21 Expanding (1+8)^n+1 using binomial theorem 03:56 Interpreting the terms of the expansion 04:38 Proving that a given expression always leaves remainder 1 when divided by 25 05:26 Strategy to solve such problems - writing down the clues 05:57 Expanding (1+5)^n using binomial theorem 07:10 Interpreting the terms of the expansion Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://ind

Published 2025-02-23 · Watch on YouTube ↗
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