If \(\left| x \right| < 1\), then \(\frac{{{x^2}}}{2} + \frac{{2{x^3}}}{3} + \frac{{3{x^4}}}{4} + \ldots \) is equal to
1
\(\frac{x}{{1 - x}} + {\log _{\rm{e}}}\left( {1 - x} \right)\)
2
\(\frac{x}{{1 +x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\)
3
\(\frac{x}{{1 - x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\)
4
\(\frac{x}{{1 + x}} + {\log _{\rm{e}}}\left( {1 - x} \right)\)