[tex]\frac{10^{n+1}-10^n}{10^{n+1}+10^n} = \frac{10^n\cdot 10^1-10^n}{10^n\cdot10^1+10^n}= \frac{10^n(10^1-1)}{10^n(10^1+1)}=\frac{9}{11}[/tex]
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[tex]\frac{10^{n+1}-10^n}{10^{n+1}+10^n} = \frac{10^n\cdot 10^1-10^n}{10^n\cdot10^1+10^n}= \frac{10^n(10^1-1)}{10^n(10^1+1)}=\frac{9}{11}[/tex]