There's a Gamma in my Pi!

Calculus Level 4

\[\sum_{n=1}^{\infty}\;\frac{\Gamma(n)\;\Gamma(n+1)}{\Gamma(n+2)\;\Gamma(n+3)}\]

Find the value of the expression above such that \(\Gamma{(n)} \) is the Gamma function.

Give answer to three decimal places.

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