Question

The greatest coefficient in the expansion of $(1 + x)^{2n + 2}$ is

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

Answer 1

Answer: (B)

$\frac{(2n + 2)!}{\lbrack(n + 1)!\rbrack^{2}}$

Answer 2

$\because$ n is even so greatest coefficient in $(1 + x)^{2n + 2}$ is

= ${ } ^ { 2 n + 2 } C _ { n + 1 } =$ $\frac{(2n + 2)!}{\lbrack(n + 1)!\rbrack^{2}}$