$\lim _{n \rightarrow \infty} \frac{1}{n^2}\left[e^{1 / n}+2 e^{2 / n}+3 e^{3 / n}+\ldots. .+2 n e^2\right]=$

• A

  $e^2-1$
• Correct answer
  B

  $e^2+1$
• C

  $2 e^2-2$
• D

  $2 e^2+1$

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