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Solution for 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 (Commerce) 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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Mathematics Textbook for Class 11 (with solutions)
Chapter 8: Binomial Theorem
Q: 11 | Page no. 171
Solution for 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 . concept: General and Middle Terms. For the courses CBSE (Commerce), CBSE (Science), CBSE (Arts)
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