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📐 Mathematics  ·  Binomial Theorem  ·  JEE

The 3rd term in the expansion of (1 - x)⁻¹ for |x| < 1 is:

Answer: x².

  • A
  • B x
  • C 1
  • D

Correct answer: A. x²

Explanation: (1-x)<sup>-1</sup> = 1 + x + x<sup>2</sup> + x<sup>3</sup> + ... (infinite GP). The 3rd term is x<sup>2.</sup>

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 →