<s>[INST] In the limit as t approaches infinity, what is the value of:

[itex]lim_{t\to\infty} e^{-t} (a_0 e^{i\omega t} + a_1 e^{-i\omega t} + a_2 e^{3i\omega t} + ...)[/itex]

Given: [itex]a_n = \frac{1}{2^n}[/itex] and [itex]\omega \in \mathbb{R}[/itex][/INST]