In the expansion of $(1+ax)^n$, the coefficients of $x^2$ and $x^3$ are $54$ and $108$ res

Question

In the expansion of $(1+ax)^n$, the coefficients of $x^2$ and $x^3$ are $54$ and $108$ respectively. Given that $n\ge3$ is an integer and $a>0$: find $n$ and $a$; hence find the coefficient of $x$; verify both given coefficients.

Accepted Answer

(a) $n=4,\ a=3$; (b) Coefficient of $x=12$.

Binomial Theorem

Binomial Theorem

Solution:

Solution locked