Question

The Greatest co-efficient in the expansion of $(1+x{)}^{2n+2}$ is

• A. $\frac{\left(2n\right)!}{(n!{)}^2}$
• B. $\frac{(2n+2)!}{\left(\right(n+1)!{)}^2}$
• C. $\frac{(2n+2)!}{n!(n+1)!}$
• D. $\frac{\left(2n\right)!}{n!(n+1)!}$

Answer 1

The correct option is B $\frac{(2n+2)!}{\left(\right(n+1)!{)}^2}$

Greatest coefficient of $(1+x{)}^{2n+2}$ is
${=}^{(2n+2)}{C}_{n+1}=\frac{(2n+2)!}{\left\{\right(n+1)!{\}}^2}$