Inverse Binomial Sum

Calculus Level 3

\[\displaystyle \sum_{n=3}^{\infty} \dfrac{1}{\binom{n}{3}} = \dfrac{1}{\binom{3}{3}} + \dfrac{1}{\binom{4}{3}} + \dfrac{1}{\binom{5}{3}} + \dfrac{1}{\binom{6}{3}} + \cdots = \, ? \]

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