TO INFINITY AND BEYOND!

Algebra Level pending

\(If\quad \sum _{ n=1 }^{ \infty }{ { \left( \frac { 1 }{ 2 } \right) }^{ n }\cos { \frac { 2n\pi }{ 3 } } \quad } can\quad be\quad expressed\\ in\quad the\quad form\quad -\frac { a }{ b } \quad where\quad a\quad and\quad b\quad are\quad \\ relatively\quad prime\quad integers,\quad what\quad is\quad a+b?\)

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