How to compute the following limit which is related to a series?
$$ \lim_{N\rightarrow\infty}N^2\sum^{N-1}_{k=1}\left(\frac{k}{N}\right)^{N\ln N}$$
How to compute the following limit which is related to a series?
$$ \lim_{N\rightarrow\infty}N^2\sum^{N-1}_{k=1}\left(\frac{k}{N}\right)^{N\ln N}$$