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How do I show that :

$$\lim_{n\to\infty} \frac{1}{n^{p+1}} \sum_{i=1}^{n} i^p = \frac{1}{p+1}$$

using a Riemann sum?

Thanks.

  • 0
    Did you copy the problem right? Your limit takes x going to infinity, but x doesn't appear inside the limit at all. Do you mean the limit as n-> infinity?2012-02-07
  • 0
    Do you mean $$\lim_{n\to\infty}\frac1{n^{p+1}}\sum_{i=1}^ni^p\;?$$2012-02-07

2 Answers 2