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Let the coefficient of the middle term of the binomial expansion of $(1+x)^{2 n}$ be $\alpha$ and those of two middle terms of the binomial expansion of $(1+\mathrm{x})^{2 n-1}$ be $\beta$ and $\gamma$. Which one of the $\begin{array}{ll}\text { following relations is correct? } & \end{array}$
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The correct answer is:
$\alpha=\beta+\gamma$
$\alpha={ }^{2 n} \mathrm{C}_{n}$
$\beta^{-2 n-1} \mathrm{C}_{n}$
$\gamma=^{2 n-1} \mathrm{C}_{n-1}$
$\beta+\gamma={ }^{2 n-1} \mathrm{C}_{n}+{ }^{2 n-1} \mathrm{C}_{n-1}={ }^{2 n} \mathrm{C}_{n}=\alpha$
$\beta^{-2 n-1} \mathrm{C}_{n}$
$\gamma=^{2 n-1} \mathrm{C}_{n-1}$
$\beta+\gamma={ }^{2 n-1} \mathrm{C}_{n}+{ }^{2 n-1} \mathrm{C}_{n-1}={ }^{2 n} \mathrm{C}_{n}=\alpha$
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