_ n [ 1 n + n^ 2 (n+1)^ 3 + n^ 2 (n+2)^ 3 + .+ 1 8 n ] is equal to
Mathematics · JEE Main · NTA Exams — Integral Calculus
\[\lim _{n \rightarrow \infty}\left[\frac{1}{n}+\frac{n^{2}}{(n+1)^{3}}+\frac{n^{2}}{(n+2)^{3}}+\ldots .+\frac{1}{8 n}\right]\] is equal to
- \(\frac{3}{8}\)
- \(\frac{1}{4}\)
- \(\frac{1}{8}\)
- none of these
Answer
(A) 3 8
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