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Maths Binomial Theorem & Mathematical Induction Mix Numeric Response

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If – + +….. + (–1) n = , then n is …………….

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The correct answer is:

Ans. 1999

Sol. (1 – x) n = n C 0 – n C 1 x + n C 2 x 2 – ……. n C n x n

multiplying both sides by x

x(1 – x) n = n C 0 x – n C 1 x 2 + n C 2 x 3 – ……. n C n x n+1

Integrating both sides

= + n C 2 x 3 +……+ n C n x n+1

= – + ….

⇒ = i.e. n = 1999

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