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a-set-S-R-and-S-n-n-2-1-n-N-n-1-show-that-minS-1-2-and-supS-1-




Question Number 129337 by TITA last updated on 15/Jan/21
a set S⊂R   and  S={(n/( (√(n^2 +1)))): n∈N, n≥1}  show that minS=(1/( (√2)))  and  supS=1
$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}\subset\mathbb{R}\:\:\:\mathrm{and}\:\:\mathrm{S}=\left\{\frac{\mathrm{n}}{\:\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}}:\:\mathrm{n}\in\mathbb{N},\:\mathrm{n}\geqslant\mathrm{1}\right\} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{minS}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\mathrm{and}\:\:\mathrm{supS}=\mathrm{1} \\ $$
Commented by TITA last updated on 15/Jan/21
please help
$$\mathrm{please}\:\mathrm{help} \\ $$

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