_n 1^p+2^p+3^p++n^pn^p+1 is:

Question

$\displaystyle\lim_{n	o\infty} \dfrac{1^p+2^p+3^p+\cdots+n^p}{n^{p+1}}$ is:

Accepted Answer

$\lim_{n	o\infty}\sum_{r=1}^n \dfrac{r^p}{n^p\cdot n} = \int_0^1 x^p\,dx = \left[\dfrac{x^{p+1}}{p+1}ight]_0^1 = \dfrac{1}{p+1}$

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