Question

The sum of the coefficients of odd powers of $x$ in the expansion of $(1+x+x^2+x^3{)}^5$ is

• A. $510$
• B. $512$
• C. $521$
• D. $522$

Answer 1

The correct option is B $512$

Sum of the coefficient of odd powers of $x$ in $f\left(x\right)$ is
$\frac{f\left(1\right)+f(-1)}{2}=\frac{(1+1+1+1{)}^5+(1-1+1-1{)}^5}{2}$
$=\frac{4^5}{2}=512$