In the expansion ${{\left( 2{{x}^{2}}+\frac{3}{x} \right)}^{n}}$, in descending powers of $x$, t

Question

In the expansion ${{\left( 2{{x}^{2}}+\frac{3}{x} \right)}^{n}}$, in descending powers of $x$, the ratio of the coefficients of the third and first term is $81:1$. Find the value of $n$.[3] Write down the first three terms of the expansion.[2] Find the term that is independent of $x$.[2]

Accepted Answer

(i) $n=9$ (ii) $512x^{18}+6912x^{15}+41472x^{12}+\cdots$ (iii) $489888$

2016 HIHS AM P2 Q3

2016 HIHS AM P2 Q3

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