7/ $\lim\dfrac{2^n+5^{n+1}}{1+5^n}$
$= \lim\dfrac{2^n+5^n.5}{1+5^n}$
$= \lim\dfrac{\Big(\dfrac{2}{5}\Big)^n+5}{\Big(\dfrac{1}{5}\Big)^n+1}$
$= \lim\dfrac{5}{1} =5$
8/ $\lim\dfrac{1.2.3^n-7^n}{5^n+2.7^n}$
$= \lim\dfrac{\Big(\dfrac{1}{7}\Big)^n+2.\Big(\dfrac{3}{7}\Big)^n-1}{\Big(\dfrac{5}{7}\Big)^n+2}$
$= \lim\dfrac{-1}{2} = \dfrac{-1}{2}$
9/$\lim\dfrac{1-2.3^n+6^n}{2^n.(3^{n+1}-5)}$
$= \lim\dfrac{1-2.3^n+6^n}{2^n.3^n.3-2^n.5}$
$= \dfrac{\Big(\dfrac{1}{6}\Big)^n-2.\Big(\dfrac{3}{6}\Big)^n+1}{3-\Big(\dfrac{2}{6}\Big)^n.5}$
$= \lim\dfrac{1}{3} = \dfrac{1}{3}$
