\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{{{1}^{3}}+{{n}^{3}}}+\frac{4}{{{2}^{3}}+{{n}^{3}}}+....+\frac{1}{2n}\]is equal to [RPET 1997]

\[\frac{1}{3}{{\log }_{e}}\frac{1}{3}\]

\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{{{1}^{3}}+{{n}^{3}

1.	\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{{{1}^{3}}+{{n}^{3}}}+\frac{4}{{{2}^{3}}+{{n}^{3}}}+....+\frac{1}{2n}\]is equal to [RPET 1997]
A.	\[\frac{1}{3}{{\log }_{e}}3\]
B.	\[\frac{1}{3}{{\log }_{e}}2\]
C.	\[\frac{1}{3}{{\log }_{e}}\frac{1}{3}\]
D.	None of these
Answer» C. \[\frac{1}{3}{{\log }_{e}}\frac{1}{3}\]

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\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{{{1}^{3}}+{{n}^{3}}}+\frac{4}{{{2}^{3}}+{{n}^{3}}}+....+\frac{1}{2n}\]is equal to [RPET 1997]

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