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Question-149660




Question Number 149660 by fotosy2k last updated on 06/Aug/21
Answered by JDamian last updated on 06/Aug/21
lim_(x→∞) ((a^(n+1) /(a^n +b^n ))+(b^(n+1) /(a^n +b^n )))=  =lim_(x→∞) (a/(1+((b/a))^n ))  + lim_(x→∞) (b/(1+((a/b))^n ))=  = 0 + b = b
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{a}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }+\frac{{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} }\right)= \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{a}}{\mathrm{1}+\left(\frac{{b}}{{a}}\right)^{{n}} }\:\:+\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{b}}{\mathrm{1}+\left(\frac{{a}}{{b}}\right)^{{n}} }= \\ $$$$=\:\mathrm{0}\:+\:{b}\:=\:\boldsymbol{{b}} \\ $$
Commented by fotosy2k last updated on 06/Aug/21
thank you
$${thank}\:{you} \\ $$

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