\[1+\frac{{{\log }_{e}}x}{1\,!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2\,!}+\frac{{{({{\log }_{e}}x)}^{3}}}{3\,!}+.....\infty =\] [Kurukshetra CEE 1998; JMI CET 2000]

\[1+\frac{{{\log }_{e}}x}{1\,!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2\,!}+

1.	\[1+\frac{{{\log }_{e}}x}{1\,!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2\,!}+\frac{{{({{\log }_{e}}x)}^{3}}}{3\,!}+.....\infty =\] [Kurukshetra CEE 1998; JMI CET 2000]
A.	\[{{\log }_{e}}x\]
B.	\[x\]
C.	\[{{x}^{-1}}\]
D.	\[-{{\log }_{e}}(1+x)\]
Answer» C. \[{{x}^{-1}}\]

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\[1+\frac{{{\log }_{e}}x}{1\,!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2\,!}+\frac{{{({{\log }_{e}}x)}^{3}}}{3\,!}+.....\infty =\] [Kurukshetra CEE 1998; JMI CET 2000]

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