Question 23
The sequence $(x_n)_{n \ge 2}$ is given by
$$
x_n = \frac{e^{1/n} - 1}{e^{1/n^2} - 1} - n.
$$
Prove that $\lim_{n \to \infty} x_n = 1/2$ and compute $\lim_{n \to \infty} n(x_n - 1/2)$.
$$
x_n = \frac{e^{1/n} - 1}{e^{1/n^2} - 1} - n.
$$
Prove that $\lim_{n \to \infty} x_n = 1/2$ and compute $\lim_{n \to \infty} n(x_n - 1/2)$.