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