### Subsequences

Posted:

**Sat Jan 20, 2018 5:16 am**Prove that the sequence $\alpha_n=\lfloor{\rm{e}}^n\rfloor\,,\; n\in\mathbb{N}$, where $\lfloor{\cdot}\rfloor$ is the floor function, has a subsequence with all its terms to being odd numbers and a subsequence with all its terms to being even numbers.

Note: I don't have a solution.

Note: I don't have a solution.