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Question Number 128232 by math35 last updated on 05/Jan/21

$$1.\mathrm{For}\mathrm{n}\in \mathbb{N},\mathrm{define}{\mathrm{s}}_{\mathrm{n}}=1+2^{2^{\mathrm{n}}}+2^{2^{\mathrm{n}+1}}.\mathrm{Which}\mathrm{of}$$ $$\mathrm{the}\mathrm{following}\mathrm{is}\mathrm{false}\mathrm{for}\mathrm{some}\mathrm{values}\mathrm{of}\mathrm{n}\in \mathbb{N}?$$ $$\mathrm{A}.3\mid {\mathrm{s}}_{\mathrm{n}}$$ $$\mathrm{B}.7\mid {\mathrm{s}}_{\mathrm{n}}$$ $$\mathrm{C}.{\mathrm{s}}_{\mathrm{n}}\mid {\mathrm{s}}_{\mathrm{n}+1}$$ $$\mathrm{D}.{\mathrm{s}}_{\mathrm{n}}^2>{\mathrm{s}}_{\mathrm{n}+1}$$ $$\mathrm{E}.{12\mathrm{s}}_1{\mathrm{s}}_2...{\mathrm{s}}_{\mathrm{n}}<{\mathrm{s}}_{\mathrm{n}+1}$$

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