Question

${lim}_{n\to \infty }{\sum }_{r=1}^n\frac{1}{n}{e}^{\frac{r}{n}}$ is

• A. e
• B. e - 1
• C. 1 - e
• D. 1 + e

Answer 1

The correct option is B e - 1

${lim}_{n\to \infty }{\sum }_{r=1}^n\frac{1}{n}{e}^{\frac{r}{n}}={\int }_0^1{e}^{x}dx=[e^x{]}_0^1=e-1$