Question

The sum of coefficients of the two middle terms in the expansion of (1 + x)^2n–1 is equal to ^2n–1C_n. 

Options

• True

• False

Answer 1

This statement is False.

Explanation:

The given expression is (1 + x)^2n–1 

Number of terms = 2n – 1 + 1 = 2n  ....(Even)

∴ Middle terms are `(2"n")/2` th term and `((2"n")/2 + 1)^"th"` terms

= n^th terms and (n + 1)^th terms

Coefficient of nth term = ^2n–1C_n–1

And he coefficient of (n + 1)^th term = ^2n–1C_n

Sum of the coefficients = `""(2n + 1)C_(n - 1) + ""^(2n - 1)C_n`

= `""^(2n - 1)C_(n - 1) + ""^(2n - 1)C_n`

= `""^(2n - 1 + 1)C_n`

= ²ⁿC_n