Представить выражение в виде степени 3: [tex]\frac{3^{-n} + 1}{3^{n} + 1}[/tex]. Created by angryfukse. algebra-ru

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AntVa

$\frac{3^{-n}+1}{3^{n}+1}=\frac{\frac{1}{3^{n}}+1}{3^{n}+1}=\frac{\frac{1+3^{n}}{3^{n}}}{3^{n}+1}=\frac{1+3^{n}}{3^{n}\cdot (3^{n}+1)}=\frac{1}{3^{n}}=3^{-n}$

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$\frac{3^{-n}+1}{3^{n}+1}=(\frac{1}{3^{n}}+1):(3^{n}+1)=(\frac{3^{n}+1}{3^{n}})*\frac{1}{3^{n}+1}=\frac{1}{3^{n}}=3^{-n}$

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