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Can the exact expression for the following series be found, given $|x|<1$? Just curious.
Separate the first term and factor out a common term, and you find that
\begin{align*} f(x) &= \frac{x^2}{17} + \frac{x^3}{3}\left(1 + x + x^2 + \dots\right) \\ &= \frac{x^2}{17} + \frac{x^3}{3} \frac{1}{1 - x} \end{align*}
from the closed form of a geometric series.
Required, but never shown
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