Question

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

• A. 256
• B. 512
• C. 1024
• D. None

Answer 1

The correct option is B

512

Let
$(1+x+x^2+x^3{)}^5=a_0+a_{1}x+a_2{x}^2+\cdots +a_{15}{x}^{15}$
Putting x=1 and -1, we get
$a{­}_0+a_1+a_2+\cdots a_{15}=4^5$
$a{­}_0-a_1+a_2-\cdots -a_{15}=0$
$\therefore a_0+a_2+a_4+....=\frac{1}{2}\times 4^5=512$