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📐 Mathematics  ·  Binomial Theorem  ·  JEE

Expand (1.01)⁵ approximately using binomial theorem (first two terms):

Answer: 1.05.

  • A 1.01
  • B 1.15
  • C 1.50
  • D 1.05

Correct answer: D. 1.05

Explanation: (1+0.01)<sup>5</sup> approx 1 + 5(0.01) = 1.05 (first two terms of binomial expansion, higher powers negligible).

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 →