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If $A$ and $B$ denote the coefficients of $x^{n}$ in the binomial expansions of $(1 + x)^{2 n}$ and $(1 + x)^{2 n - 1}$ respectively, then

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A= B

2A = B

A= 2B

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detailed solution

Correct option is C

We have ,A = Coefficient of xn in (1+x)2n⇒A=2nCn⇒A=2nn2n−1Cn−1=22n−1Cn−1∵nCr=nrn−1Cr−1and , B = Coefficient of xn in (1+x)2n−1⇒B=2n−1Cn=2n−1Cn−1 ∵nr=nCn−rClearly, A = 2B.

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If A and B denote the coefficients of xn in the binomial expansions of (1+x)2n and (1+x)2n−1respectively, then

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Ready to Test Your Skills?

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If $A$ and $B$ denote the coefficients of $x^{n}$ in the binomial expansions of $(1 + x)^{2 n}$ and $(1 + x)^{2 n - 1}$ respectively, then