q$8$ If a sequence $c_1,c_2,c_3,$dots has limit $K$ then the sequence $e^{c_1},e^{c_2},e^{c_3},$dots has limit $e^K.$ Use this fact together with l'Hopital's rule to compute the limit of the sequence given by

$b_n=(1+\frac{4\mathrm{.}4}{n}{)}^n$