# Coefficient of expansion and limits

Let $${ A }_{ n }$$ be the coefficient of $${x}^{-n+3}$$ in the expansion of $$\left(x+ \frac {1}{x} \right)^{n+1}$$. Determine the value of $$\displaystyle{\sum _{ n=1 }^{ \infty }}{ \frac { 1 }{ { A }_{ n } } } ,$$ where $$n$$ is a positive integer.

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