In the binomial expansion of ${{\left( 2-kx \right)}^{n}},$where $n\ge 3$ and $k$ is a constan

Question

In the binomial expansion of ${{\left( 2-kx \right)}^{n}},$where $n\ge 3$ and $k$ is a constant, the coefficients of $x$ and ${{x}^{2}}$ are equal. Express $k$ in terms of $n.$

Accepted Answer

$k=0$ or $k=-\frac4{n-1}$, for $n\ge3$.

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

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