A crazy series, maybe

Calculus Level 4

\[ \binom{3}{3} + \binom{5}{3}\frac {1}{ 2 } + {7 \choose 3}\frac {1}{ 2^2 } + {9 \choose 3}\frac {1}{ 2^3 } + {11 \choose 3 }\frac {1}{ 2^4 } + \ldots = \ ? \]

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