Mathematics - Binomial Theorem Question with Solution | TestHub

The coefficient of $x^6$ is found by identifying combinations of exponents that sum to 6. We consider the expression $(1+x)(1+x^2{)}^2(1+x^3{)}^3\dots (1+x^n{)}^n$. The combinations are: $6$, $1+5$, $2+4$, $3+3$, $1+2+3$. The coefficient is the number of ways to obtain $x^6$, which is $1+2+3+3+2\ast 3=28$.

Therefore, the coefficient of $x^6$ is 28.