Question

The coefficient of $t^7$ in $(1+t{)}^6\left(1+t^2\right)\left(1+t^4\right)\left(1+t^8\right)$ is divisible by

• A. 4
• B. 6
• C. 8
• D. 16

Answer 1

Answer: (A), (C), (D)

Coefficient of $t^7\text{ in }(1+t^6\left[1+t^2+t^4+t^6+t^8+\dots .\right]$
$={}^6{C}_5+{}^6{C}_3+{}^6{C}_1=32$