In the expansion of (1 + x) n , prove that C 0 + + + + .…

Maths Binomial Theorem & Mathematical Induction Mix Numeric Response

Published by: CGP EDU Academic Team

Published on: August 12, 2026

In the expansion of (1 + x) n , prove that C 0 + + + + ........ + =

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The correct answer is:

Sol. (1 + x) n = C 0 + C 1 x + C 2 x 2 + ..... C n x n Integrating with respect to 'x' in (0 to 1)

dx = dx

C 0 + C 1 /2 + C 2 /3 + C 3 /4 + ......... + C n /n+1 = 2 n+1 –1/n+1

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