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Prove that the Coefficient of Xn in the Expansion of (1 + X)2n is Twice the Coefficient of Xn in the Expansion of (1 + X)2n–1 . - CBSE (Arts) Class 11 - Mathematics

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Question

Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n–1 .

Solution

Comparing the indices of x in xn and in Tr + 1, we obtain

r = n

Therefore, the coefficient of xn in the expansion of (1 + x)2n is

Therefore, the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n–1.

Hence, proved.

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Solution Prove that the Coefficient of Xn in the Expansion of (1 + X)2n is Twice the Coefficient of Xn in the Expansion of (1 + X)2n–1 . Concept: General and Middle Terms.
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