The coefficient of x4 in the expansion of (1 + 5 x + 9 x2 + 13 x3 + 17 x4 + . ldots ldots )(1 + x2)11 is equal to

Question

The coefficient of x4 in the expansion of (1 + 5 x + 9 x2 + 13 x3 + 17 x4 + . ldots ldots )(1 + x2)11 is equal to (A) 11C2+411C1+3 (B) 11C2+311C1+4 (C) 311C2+411C1+3 (D) 171

Tardigrade Admin · Accepted Answer

Coefficient of x4 in (1+5 x+9 x2+13 x3+17 x4+ ldots ldots .)(1+11 x2+ 11 C2 x4+ ldots ldots) Coefficient of x4 is = 11 C2+9 × 11+17 × 1 =(11 × 10/2)+99+17 =55+99+17 =171

Q. The coefficient of $x^{4}$ in the expansion of $(1 + 5 x + 9 x^{2} + 13 x^{3} + 17 x^{4} + . \dots\dots) (1 + x^{2})^{11}$ is equal to

$^{11} C_{2} + 4^{11} C_{1} + 3$

$^{11} C_{2} + 3^{11} C_{1} + 4$

$3^{11} C_{2} + 4^{11} C_{1} + 3$

$171$

Coefficient of $x^{4}$ in $(1 + 5 x + 9 x^{2} + 13 x^{3} + 17 x^{4} + \dots\dots .) (1 + 11 x^{2} +^{11} C_{2} x^{4} + \dots\dots)$
Coefficient of $x^{4}$ is $=^{11} C_{2} + 9 \times 11 + 17 \times 1$
$= \frac{11 \times 10}{2} + 99 + 17$
$= 55 + 99 + 17$
$= 171$

Q. The coefficient of x4 in the expansion of (1+5x+9x2+13x3+17x4+.……)(1+x2)11 is equal to

11C2​+411C1​+3

11C2​+311C1​+4

311C2​+411C1​+3

171