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# Find an expression, in terms of n, for the coefficient of x in the expansion $(1+4 x)+(1+4 x)^{2}+(1+4 x)^{3}+\ldots+(1+4 x)^{n}$.

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We're given a series of binomial terms raised to a certain positive integer that can be expanded using the binomial theorem. Given the expression below, we're asked to create an expression that can be used to determine the coefficient of its $x$ in terms of $n$.

$\left(1+4x\right)^{}+\left(1+4x\right)^{2}+\left(1+4x\right)^{3}+...+\left(1+4x\right)^{n}$

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