Linearity and time-shifting of $\mathcal{F}\{0.8^n\cos(0.1πn)u[n]\}$
$\displaystyle \hbox{ DTFT}(\alpha x_1 + \beta x_2) = \alpha\cdot \hbox{ DTFT}(x_1) + \beta \cdot\hbox{ DTFT}(x_2)$

Linearity property cannot applied here.