Question

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 + γ

b. α < β + γ

c. α = β + γ

d. α = βγ

Answer 1

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