Evaluate $$\lim_{n\to \infty}\frac{n+n^2+n^3+....+n^n}{1^n+2^n+3^n+....+n^n}$$
My Attempt
Was able to write as $$\lim_{n\to \infty}\frac{\frac{n^n-1}{n-1}}{n^n(\frac{1}{n})\sum_{r=1}^n\left(\frac{r}{n}\right)^n}$$
But not sure how to take it further though the denominator appears to be Riemann Sum
