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

\(\frac{x}{{1 +x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\)

\(\frac{x}{{1 - x}} + {\log _{\rm{e}}}\left( {1 - x} \right)\)

\(\frac{x}{{1 - x}} + {\log _{\rm{e}}}\left( {1 + x} \right)\)

\(\frac{x}{{1 + x}} + {\log _{\rm{e}}}\left( {1 - x} \right)\)

If \(\left| x \right| < 1\), then \(\frac{{{x^2}}}{2} + \frac{{2{x^3

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

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

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