Given the binomial expansion of $(1+x)^n$, can we find $x$ and $n$?

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

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

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