Question

The sum of coefficients of the two middle terms in the expansion of $(1+x{)}^{2n-1}$ is equal to

• A. $(2n-1)C_n$
• B. ${}^{(2n-1)}{C}_{n+1}$
• C. ${}^{2n}{C}_{n-1}$
• D. ${}^{2n}{C}_n$

Answer 1

The correct option is D ${}^{2n}{C}_n$

$(1+x{)}^{2n-1}$ has $2n$ terms.

Hence there are $2$ middle terms, the $n^{th}$ term and the $(n+1{)}^{th}$ term.

$t_n=(2n-1)C_{n-1}\cdot x^{n-1}$

$t_{n+1}=(2n-1)C_{n+1-1}{x}^{n+1-1}=2n{C}_n{x}^n$

Sum of coefficients$=(2n-1)C_{n-1}+(2n-1)C_n=2n{C}_n$.