How to evaluate: $\lim\limits_{n\to\infty} \frac{1^{p-1}+2^{p-1}+...+n^{p-1}}{n^p}$

Hint:

Just write $$\dfrac{1^{p-1}+2^{p-1}+...+n^{p-1}}{n^p} = \frac{1}{n}\sum_{k=1}^n\left(\frac{k}{n}\right)^{p-1}$$ and handle it as the limit of a Riemann sum.

Tags:

Limits

Analysis

Calculus

Limits Without Lhopital

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