Evaluate-the-limit-and-prove-by-the-definition-that-as-n-for-z-1-2-z-1-n-1-n-z-2-

Question Number 155585 by mathdanisur last updated on 02/Oct/21

$$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{by}\:\mathrm{the} \\ $$$$\varepsilon−\delta\:\mathrm{definition}\:\mathrm{that}\:\mathrm{as}\:\mathrm{n}\rightarrow\infty\:\mathrm{for}\:\mathrm{z}\geqslant\mathrm{1} \\ $$$$\left(\mathrm{2}\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{z}}\:−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:\rightarrow\:\mathrm{z}^{\mathrm{2}} \\ $$

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