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Question-152376




Question Number 152376 by fotosy2k last updated on 27/Aug/21
Commented by fotosy2k last updated on 28/Aug/21
pls help
$${pls}\:{help} \\ $$
Answered by imjagoll last updated on 28/Aug/21
 lim_(nā†’āˆž)  ((a((a/b))^n +b)/(((a/b))^n +1)) = b    note : lim_(nā†’āˆž) ((a/b))^n =0 , a<b
$$\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{a}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{\mathrm{n}} +\mathrm{b}}{\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{\mathrm{n}} +\mathrm{1}}\:=\:\mathrm{b}\: \\ $$$$\:\mathrm{note}\::\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{\mathrm{n}} =\mathrm{0}\:,\:\mathrm{a}<\mathrm{b} \\ $$

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