Ch 7 proves the binomial theorem for positive integers and explores its applications. Students learn to expand (a+b)ⁿ, find specific terms, and use Pascal's triangle.
(a+b)ⁿ = Σ(r=0 to n) nCr aⁿ⁻ʳ bʳ = nC0 aⁿ + nC1 aⁿ⁻¹b + nC2 aⁿ⁻²b² + … + nCn bⁿ. The expansion has (n+1) terms. Coefficients are nC0, nC1, …, nCn.
The general (r+1)th term: T(r+1) = nCr aⁿ⁻ʳ bʳ. For middle term(s): if n is even, middle term = T(n/2 + 1). If n is odd, two middle terms: T((n+1)/2) and T((n+3)/2).
Download: https://ncert.nic.in/textbook/pdf/kemh107.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
Pascal's triangle is a triangular array where each number is the sum of the two numbers above it. Row n gives the binomial coefficients: nC0, nC1, nC2, …, nCn. It provides a visual way to find expansion coefficients.
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