The greatest coefficient in the expansion of (1 +x)2n+2 is

Question

The greatest coefficient in the expansion of (1 +x)2n+2 is (A) ((2n)!/(n!)2) (B) ((2n + 2)!/((n + 1)!)2) (C) ((2n + 2)!/n!(n + 1) !) (D) ((2n)!/n!(n + 1) !)

Tardigrade Admin · Accepted Answer

n2 - (4r + 1) n + 4r2 - 2 = 0 where r = 2

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

$\frac{( 2 n )!}{( n ! ) ^{2}}$

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

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

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

$n^{2} - (4 r + 1) n + 4 r^{2} - 2 = 0$ where r = 2

Q. The greatest coefficient in the expansion of (1+x)2n+2 is

(n!)2(2n)!​

((n+1)!)2(2n+2)!​

n!(n+1)!(2n+2)!​

n!(n+1)!(2n)!​

n2−(4r+1)n+4r2−2=0 where r = 2

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

$\frac{( 2 n )!}{( n ! ) ^{2}}$

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

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

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

$n^{2} - (4 r + 1) n + 4 r^{2} - 2 = 0$ where r = 2