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NDA2020MathematicsBinomial TheoremActual

What is the sum of the last five coefficients in the expansion of (1+x)^9 when it is expanded in ascending powers of x ?

Options

  1. A256
  2. B512
  3. C1024
  4. D2048

Correct answer

A. 256

Step-by-step solution

Expansion of aligned (1+x)^9= ^9 C₀ & + ^9 C₁ x+ ^9 C₂ x^2+ ^9 C₃ x^3+ ^9 C₄ x^4 & + ^9 C₅ x^5+ ^9 C₆ x^6+ ^9 C₇ x^7+ ^9 C₈ x^8+ ^9 C₉ x^9 aligned Sum of last five co-efficient aligned & = ^9 C₅+ ^9 C₆+ ^9 C₇+ ^9 C₈+ ^9 C₉ & =126+84+36+9+1=256 aligned

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