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How to compute the following limit which is related to a series?

$$ \lim_{N\rightarrow\infty}N^2\sum^{N-1}_{k=1}\left(\frac{k}{N}\right)^{N\ln N}$$

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    Hint: $n\ln n$ is asymptotically the $n$th prime number.2012-08-31
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    The 5th question of this type you have asked. Have you not learned something from the other four that you could at least try to apply to this one?2012-08-31
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    @dot, what do primes have to do with it?2012-08-31
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    the solutions of each one is different. please see the corresponding answer.2012-08-31
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    Yes, jany, the details of the solutions are different, but my question remains: have you not learned anything from the other four that could at least get you started working on this one, instead of offering it to us with no sign that you have put even the least bit of thought into it? If you aren't learning anything usable, what is the purpose of asking all the questions?2012-08-31

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