📐 Mathematics · Binomial Theorem · JEE

In the expansion of (1 + x)¹⁵, the coefficients of which two consecutive terms are equal?

Answer: x⁷ and x⁸.

A x⁶ and x⁷
B x⁷ and x⁸
C x⁸ and x⁹
D they are never equal

Correct answer: B. x⁷ and x⁸

Explanation: C(15, r) = C(15, r+1) requires r + (r+1) = 15, so r = 7; the terms are x⁷ and x⁸.

Row n of Pascal's triangle gives the coefficients nC₀, nC₁, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.

Concept context

Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term

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In the expansion of (1 + x)¹⁵, the coefficients of which two consecutive terms are equal?

Concept context

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