We know that
$\displaystyle\frac{4}{1+16x^2}=4-64x^2+1024x^4-16384x^6+...$
for $x\in\left(-\dfrac{1}{4},\dfrac{1}{4}\right)$.
**Using this fact, find the function that corresponds to the following series.**
$\displaystyle 4x-\frac{{64}}{3}x^3+\frac{1024}{5}x^5-\frac{16384}{7}x^7+...$
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