Question

The ratio of the coefficient of the middle term in the expansion of (1 + x)²⁰ and the sum of the coefficients of two middle terms in expansion of (1 + x)¹⁹ is ________.

Answer 1

Correct answer 1

Coeff. of middle term in (1 + x)²⁰ = ²⁰C₁₀ & Sum of Coeff. of two middle terms in 

(1 + x)¹⁹ = ¹⁹C₉ + ¹⁹C₁₀

So required ratio = \(\frac{^{20}C_{10}}{^{19}C_9 + ^{19}C_{10}} = \frac{^{20}C_{10}}{^{20}C_{10}} = 1\)