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📐 Mathematics  ·  Binomial Theorem  ·  JEE

Find the middle term in the expansion of (x + 1/x)⁸.

Answer: 70.

  • A 56x
  • B 8C4 / x²
  • C 70
  • D 70/x

Correct answer: C. 70

Explanation: n=8, middle term is T<sub>5</sub>. T<sub>5</sub> = 8C4 x<sup>8-4</sup> x x<sup>-4</sup> = 8C4 = 70. Middle term = 70.

Pascal's Triangle: Binomial Coefficients11112113311464115101051n=0n=1n=2n=3n=4n=5Each entry = sum of the two entries diagonally above it (Pascal's identity); row n gives nC0...nCn

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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