Question

Let $\langle x_n \rangle$ be a sequence which is given by $x_n = \frac{5^n}{n!}$, then

• A. $\langle x_n \rangle$ is not a Cauchy sequence.
• B. $\langle x_n \rangle$ is oscillate.
• C. $\langle x_n \rangle$ is convergent.
• D. $\langle x_n \rangle$ is divergent.

Hint:

Factorials grow much faster than exponentials ($n! \gg a^n$). Therefore, $\lim_{n \to \infty} \frac{a^n}{n!} = 0$ for any real constant $a$.

Answer 1

The Correct Option is C