[tex]\dfrac{2^n+2^{n+1}+2^{n+2}}{7^n+7^{n+1}+7^{n+2}}=\dfrac{2^n+2\cdot 2^n+2^2\cdot 2^n}{7^n+7\cdot 7^n+7^2\cdot 7^n}=\dfrac{2^n+2\cdot 2^n+4\cdot 2^n}{7^n+7\cdot 7^n+49\cdot 7^n}=\\\\=\dfrac{7\cdot 2^n}{57\cdot 7^n}=\dfrac{2^n}{57\cdot 7^{n-1}}.[/tex]
Green eyes.
