How to find a upper bound of the set $A= \{ (1+\frac{1}{n})^n : n \in \mathbb{N}^{*} \} $ i have the set $A= \{(1+\frac{1}{n})^{n} : n \in \mathbb{N}^* \}$ and the exercise ask me to find at least $2$ upper bound least equal to $\frac{14}{5}$.
My first question is, how i know $\frac{14}{5}$ is a upper bound of $A$?
My attempt is show doesn't exist $m \in \mathbb{N}^*$ such that $(1+\frac{1}{m})^{m} = \frac{14}{5}$, but i'm stuck,  for the other upper bound numbers, i could reason the same way?
Thanks for suggestions

Actually, the upper bound of this sequence is the standard definition of $e$. More formally,
$$
e=\lim_{n\to\infty} (1+{1\over n})^n\approx 2.71828182846
$$
To reject $14\over 5$ as an upper bound, note that $e< 14/5$.
