The binomial expansion of \((1+x)^n\) is

\[1-\dfrac{2}{3}\times \dfrac{1}{3} + \dfrac{\frac{1}{2}\times\frac{3}{2}}{1\times 2}\left(\dfrac{1}{3}\right)^2- \dfrac{\frac{1}{2}\times\frac{3}{2}\times\frac{5}{2}}{1\times 2\times 3}\left(\dfrac{1}{3}\right)^3+...\]

Determine the values of \(x\) and \(n\).

Could we write out the expansion of \((1+x)^n\) and compare the terms with what we are given?