If xp occurs in the expansion of x 2 - 1 x 2n- prove that its coefficient is - 2n - 4n-p 3 - 2n-p 3 - -

(x^2 + 1x)^2n T_r + 1 = ^2n Cr (x^2)^2n r(1x)^r T_r +1 = ^2n Cr x^4n 2r r T_r + 1 = ^2n Cr x^4n 3r 4n 3r = p ⇒ 4n p ...

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Binomial Coefficients

If xp occur...

Question

If $x^{p}$ occurs in the expansion of ${(x^{2} + \frac{1}{x})}^{2 n}$ , prove that its coefficient is $⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{(2 n)!}{(\frac{4 n - p}{3})! (\frac{2 n + p}{3})!} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$

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x^{p}

{(x^{2} + \frac{1}{x})}^{2 n}

\frac{(2 n)!}{(\frac{4 n - p}{3})! (\frac{2 n + p}{3})!}

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