Evaluate the limit as n approaches infinity of the sum ∑_(r=1)ⁿ (1)/(n) e^(r/n).
e + 1
e - 1
1 - e
e
Correct answer: e - 1
Solution
The limit can be interpreted as a Riemann sum for the function e^x over the interval [0, 1]. As n approaches infinity, the sum converges to the integral of e^x from 0 to 1, which evaluates to e - 1.