The value of \( \lim _{n \rightarrow \infty} \frac{1 \cdot n+2 \cdot(n-1)+3 \cdot(n-2)+\ldots+n ...

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The value of \( \lim _{n \rightarrow \infty} \frac{1 \cdot n+2 \cdot(n-1)+3 \cdot(n-2)+\ldots+n \cdot 1}{1^{2}+2^{2}+\ldots+n^{2}} \) is
(a) 1
(b) \( -1 \)
(c) \( \frac{1}{\sqrt{2}} \)
(d) \( \frac{1}{2} \)
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