Find the coefficient of x−2 in the expansion of (x2+x54)6.

In the expansion (axp+xqb)n, the term containing xk is Tr+1 where r=p+qnp−k.Here, r=5+212+2=2.T2+1=T3=6C2(x2)4(x54)2=6C2(16)x−2=(15)(16)x−2Therefore, required coefficient = 240.

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Find the coefficient of x^{-2} in the expansion of (x^2+{4}{x^

Question

Find the coefficient of $x^{- 2}$ in the expansion of $(x^{2} + \frac{4}{x ^{5}})^{6}$ .

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Find the coefficient of

x^{- 2}

in the expansion of

(x^{2} + \frac{4}{x ^{5}})^{6}

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

In the expansion

(a x^{p} + \frac{b}{x ^{q}})^{n}

, the term containing

x^{k}

T_{r + 1}

where

r = \frac{n p - k}{p + q}

Here,

r = \frac{12 + 2}{5 + 2} = 2

T_{2 + 1} = T_{3} = 6_{C}_{2} (x^{2})^{4} (\frac{4}{x ^{5}})^{2}

= 6_{C}_{2} (16) x^{- 2}

= (15) (16) x^{- 2}

Therefore, required coefficient = 240.

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Question Text	Find the coefficient of $x^{- 2}$ in the expansion of $(x^{2} + \frac{4}{x ^{5}})^{6}$ .
Answer Type	Text solution:1
Upvotes	150

Find the coefficient of x−2 in the expansion of (x2+x54​)6.

Text solutionVerified

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Find the coefficient of $x^{- 2}$ in the expansion of $(x^{2} + \frac{4}{x ^{5}})^{6}$ .