find the limit of the following sequence or determine that the sequence diverges. { ( 1 - 20 / n ) ^ n }…

Explanation:

Step1: Recall the limit formula

We know the well - known limit formula $\lim_{n\rightarrow\infty}(1 + \frac{a}{n})^n=e^{a}$. Here, our sequence is $a_n=(1-\frac{20}{n})^n$. Let $m=-n$ and $b = 20$. Then as $n\rightarrow\infty$, $m\rightarrow-\infty$. And $(1-\frac{20}{n})^n=\left(1+\frac{(- 20)}{n}\right)^n$.

Step2: Calculate the limit

By the formula $\lim_{n\rightarrow\infty}(1+\frac{a}{n})^n = e^{a}$, when $a=-20$, we have $\lim_{n\rightarrow\infty}(1-\frac{20}{n})^n=e^{-20}=\frac{1}{e^{20}}$.

Answer:

A. The limit of the sequence is $\frac{1}{e^{20}}$