In the binomial expansion of ${{\left( 1+kx \right)}^{n}}$, where $n\ge 3$ and $k$ is a consta

Question

In the binomial expansion of ${{\left( 1+kx \right)}^{n}}$, where $n\ge 3$ and $k$ is a constant, the coefficient of ${{x}^{3}}$ and ${{x}^{4}}$ are equal. Express $k$ in terms of $n.$

Accepted Answer

For $n=3$: $k=0$. For $n>3$: $k=0$ or $k=\frac4{n-3}$.

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

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