The value of \[ \lim _{n \rightarrow \infty} \frac{\left(1^{2}+2^{2...

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The value of
\[
\lim _{n \rightarrow \infty} \frac{\left(1^{2}+2^{2}+\ldots+n^{2}\right)\left(1^{3}+2^{3}+\ldots+n^{3}\right)\left(1^{4}+2^{4}+\ldots+n^{4}\right)}{\left(1^{5}+2^{5}+\ldots+n^{5}\right)^{2}}
\]
\( \mathrm{P} \) is equal to
(1) \( \frac{3}{5} \)
(2) \( \frac{4}{5} \)
(3) \( \frac{2}{5} \)
(4) \( \frac{1}{5} \)
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