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Question Number 200304 by Calculusboy last updated on 16/Nov/23

Answered by Sutrisno last updated on 17/Nov/23

$${lim}_{n\to \mathrm{\infty }}0.2^{{log}_{\sqrt{5}}\left(\frac{\frac{1}{4}}{1-\frac{1}{2}}\right)}$$$${lim}_{n\to \mathrm{\infty }}0.2^{{log}_{\sqrt{5}}\left(\frac{1}{3}\right)}$$$${lim}_{n\to \mathrm{\infty }}0.2^{{log}_{0.2}{\left(\frac{1}{3}\right)}^2}$$$$=\frac{1}{9}$$

Commented by Calculusboy last updated on 28/Nov/23

$$\mathit{t}\mathit{h}\mathit{a}\mathit{n}\mathit{k}\mathit{s}\mathit{s}\mathit{i}\mathit{r}$$

Answered by MathematicalUser2357 last updated on 05/Jan/24

$$=\underset{n\to \mathrm{\infty }}{\lim 0}.2^{{\log }_{\sqrt{5}}\frac{1}{2}}$$$$=\underset{n\to \mathrm{\infty }}{\lim 0}.2^{-\frac{1}{2}{\log }_{\frac{1}{5}}\frac{1}{2}}$$$$=\frac{\sqrt{5}}{2}$$

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