Calculate limit of a sum I'm currently repeating for exam and i'm stuck with limits of following two sums.
$$\lim_{n\rightarrow +\infty} \sum_{k=0}^n \frac{(k-1)^7}{n^8}$$
and
$$\lim_{n\rightarrow +\infty} \sum_{k=0}^n \frac{\sqrt[n]{e^k}}{n}$$
Maybe if sum were from $k=0$ to $\infty$ then i could change it to integral and then calculate it somehow, but i this is a first time i see such task and i'd be greatful for ideas how to solve such tasks... 
Thank you in advance!

Hints:
$$\sum_{k=0}^n\frac{\sqrt[n]{e^k}}n=\frac1n\sum_{k=0}^ne^{k/n}\xrightarrow[n\to\infty]{}\int\limits_0^1e^x\,dx$$
I'm assuming the first sum actually begins at $\;k=1\;$ :
$$\sum_{k=1}^n\frac{(k-1)^7}{n^8}=\frac1n\sum_{k=0}^n\left(\frac kn\right)^7\xrightarrow[n\to\infty]{}\int\;\ldots$$
