We know that
$\displaystyle\frac{3}{1+3x}=3-9x+27x^2-81x^3+...$
for $\displaystyle x\in\left(-\frac{1}{3},\frac{1}{3}\right)$.
**Using this fact, find the function that corresponds to the following series.**
$\displaystyle 3x-\frac{9}{2}x^2+9x^3-\frac{81}{4}x^4+...$
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