The Maclaurin power-series for the function \(f\) is given by \(\displaystyle f(x)=\sum_{n=0}^\infty \left(-\frac{x}{4} \right)^n\). What is the value of \(f(3)\) ?

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The power-series represents the sum of the geometric power-series with starting value \(a_1=1\) and ratio \(-\dfrac{x}{4}\):

$$ S_n= \frac{a_1}{1-r}=\frac{1}{1-\left(-\frac{x}{4}\right)} $$ $$ f(3) = \frac{1}{1-\left(-\frac{3}{4}\right)} $$ $$ = \frac{1}{\frac{7}{4}} $$ $$ = \boxed{\frac{4}{7}} $$