$$ \operatorname{Lim}_{n \rightarrow \infty} \frac{1^p+2^p+3^p+\ldots+n^p}{n^{p+1}} $$ is

• Correct answer
  A

  $\frac{1}{p+1}$
• B

  $\frac{1}{1-p}$
• C

  $\frac{1}{p}-\frac{1}{p-1}$
• D

  $\frac{1}{p+2}$

Hence, the correct answer is option: 'A'.