Let the coefficient of the middle term of the binomial expansion of (1

1.	Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α > β + γb. α < β + γc. α = β + γd. α = βγ
Answer» Correct option c. α = β + γ Explanation: α = ²ⁿC_n β = ^{2n - 1}C_n γ =^{2n - 1}C_{n - 1} β + γ = ^{2n - 1}C_n + ^{2n - 1}C_{n - 1} = ²ⁿC_n = α

Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α > β + γb. α < β + γc. α = β + γd. α = βγ

Answer»

Correct option c. α = β + γ

Explanation:

α = ²ⁿC_n

β = ^{2n - 1}C_n

γ =^{2n - 1}C_{n - 1}

β + γ = ^{2n - 1}C_n + ^{2n - 1}C_{n - 1} = ²ⁿC_n = α

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Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α &gt; β + γb. α &lt; β + γc. α = β + γd. α = βγ

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Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be α and those of two middle terms of the binomial expansion of (1 + x)2n – 1 be β and γ. Which one of the following relations is correct? a. α > β + γb. α < β + γc. α = β + γd. α = βγ