Zaymiey

📐 Mathematics  ·  Binomial Theorem  ·  JEE

The middle term in the expansion of (2x − 1/x)⁸ is:

Answer: 1120.

  • A 1120
  • B −1120
  • C 560
  • D 70

Correct answer: A. 1120

Explanation: With n = 8 the middle term is the 5th (r = 4): C(8,4)(2)⁴(−1)⁴ = 70·16 = 1120.

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

Read the full Binomial Theorem notes →