A Geometric or Harmonic Series?

Calculus Level 3

\[\large \frac{x^1}{1}+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+\ldots\]

Find the closed form of the sum above, where \(-1≤x<1\).

\[\frac{2x-x^2}{{(1-x)}^2}\] \[-\ln{(1-x)}\] \[\tan{x}\] \[\sin{x}\] \[\frac{x}{1-x}\] Divergent sum \[\frac{1}{{(1-x)}^2}\] \[e^x-1\]

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