I'm having a little trouble with a question that requires me to interpret a limit as a Riemann sum for an integral. However, I'm having trouble identifying which aspects of the limit correspond to the parts of the function I need to know to relate it to an integral.
The limit is as follows: $\lim_{n\to\infty}\frac{(\sqrt[n]e)+(\sqrt[n]e^2)+…+(\sqrt[n]e^{2n})}{n}$
I'm not entirely sure how to proceed. I know that $1/n=Δx$ but I don't know which function the integral is representing.
Best Answer
Hint: the limit can be written as $\lim_{n\to\infty}2\sum_{k=1}^{2n} e^{2\frac{k}{2n}}\frac{1}{2n}$. Is it more clear now?