In the expansion of ${{\left( 2x+\frac{k}{x} \right)}^{13}}$, where $k$ is a positive constant,

Question

In the expansion of ${{\left( 2x+\frac{k}{x} \right)}^{13}}$, where $k$ is a positive constant, the ratio of the coefficient of ${{x}^{3}}$ to the coefficient of $\frac{1}{x}$ is $3:2$. Find the value of $k$.

Accepted Answer

$k=\sqrt{2}$

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

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