Weird limit: $\lim_{n\to\infty} \,\sum_{k=1}^n\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$ https://ift.tt/eA8V8J

I came across the following problem recently:

Evaluate $$\lim_{n\to\infty} \,\sum_{k=1}^n\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$$

I tried to rewrite the inner sum as a Riemann sum hoping that the limit would become a definite integral, but no gain. Please help!

from Hot Weekly Questions - Mathematics Stack Exchange
Alan