\( \lim _{n \rightarrow \infty} \frac{1}{n^{3}}\left(\sqrt{n^{2}+1}+2 \sqrt{n^{2}+2^{2}}+\ldots ...
\( \lim _{n \rightarrow \infty} \frac{1}{n^{3}}\left(\sqrt{n^{2}+1}+2 \sqrt{n^{2}+2^{2}}+\ldots \ldots+n \sqrt{\left(n^{2}+n^{2}\right)}=:\right. \)
(a) \( \frac{3 \sqrt{2}-1}{2} \)
(b) \( \frac{2 \sqrt{2}-1}{3} \)
(c) \( \frac{3 \sqrt{3}-1}{3} \)
(d) \( \frac{4 \sqrt{2}-1}{2} \)
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