[tex]\it \dfrac{3\cdot4^n\cdot5^{n+2}+4^{n+1}\cdot5^{n+2}}{20^{n+1}+5\cdot20^n} = \dfrac{3\cdot4^n\cdot5^n\cdot5^2+4\cdot4^n\cdot5^n\cdot5^2}{20^n\cdot20+5\cdot20^n} =\\ \\ \\ = \dfrac{20^n\cdot75+20^n\cdot100}{20^n\cdot20+5\cdot20^n} = \dfrac{20^n(75+100)}{20^n(20+5)}=\dfrac{175}{25}=7[/tex]
