In the expansion of $\left(x^2 + \frac{1}{3x}\right)^n$ in descending powers of $x$, the coeffic

Question

In the expansion of $\left(x^2 + \frac{1}{3x}\right)^n$ in descending powers of $x$, the coefficients of the second and the third term are in the ratio of $6 : 11$. Show that the value of $n$ is $12$.[6] Find the middle term.[2] Find the coefficient of $x^6$ in the expansion of $(2 - x^3)\left(x^2 + \frac{1}{3x}\right)^{12}$.[3]

Accepted Answer

(a) $n=12$ (b) $\dfrac{308}{243}x^6$ (c) $\dfrac{176}{81}$

2023 Ahmad Ibrahim Sec AM S3 EOY Q11

2023 Ahmad Ibrahim Sec AM S3 EOY Q11

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