5 questions linked to/from Prove limit converges in definition of $e.$
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### Prove that $a_n = \{\left(1+\frac{1}{n}\right)^n\}$ is bounded sequence, $n\in\mathbb{N}$

How to prove the following: $a_n = \left\{\left(1+\frac{1}{n}\right)^n\right\}$ is bounded sequence, $n\in\mathbb{N}$