[Solution] Determine whether the series ∑limits_n=1^∞ (2• 4• 6• • • (2n))/(2)^n(n+2)! converges absolutely, conditionally,


Question: Determine whether the series

\[\sum\limits_{n=1}^{\infty }{\frac{2\cdot 4\cdot 6\cdot \cdot \cdot (2n)}{{{2}^{n}}(n+2)!}}\]

converges absolutely, conditionally, or diverges.

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