How can I find $\lim_{n\to \infty}\left(\cfrac{1^p+2^p+\cdots+ n^p}{n^p}-\cfrac{n}{p+1}\right)$?
Evaluating $\lim\limits_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$