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hi-everybody-with-n-N-prove-that-n-0-N-n-n-0-n-2-2-n-




Question Number 133279 by greg_ed last updated on 20/Feb/21
hi, everybody !  with n ∈ N,  prove that : ∃ n_0  ∈ N / ∀ n ≥ n_0  , n^2  ≤ 2^n .
$$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{n}}\:\in\:\mathbb{N}, \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\::\:\exists\:\boldsymbol{\mathrm{n}}_{\mathrm{0}} \:\in\:\mathbb{N}\:/\:\forall\:\boldsymbol{\mathrm{n}}\:\geqslant\:\boldsymbol{\mathrm{n}}_{\mathrm{0}} \:,\:\boldsymbol{\mathrm{n}}^{\mathrm{2}} \:\leqslant\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} . \\ $$

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