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Question Number 134393 by liberty last updated on 03/Mar/21

 Σ_(k=0) ^∞  ((4^k  (k!)^2 )/((2k+1)^2  (2k)!)) =?

$$\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{\mathrm{k}} \:\left(\mathrm{k}!\right)^{\mathrm{2}} }{\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} \:\left(\mathrm{2k}\right)!}\:=? \\ $$

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