Question Number 134393 by liberty last updated on 03/Mar/21
![Σ_(k=0) ^∞ ((4^k (k!)^2 )/((2k+1)^2 (2k)!)) =?](https://www.tinkutara.com/question/Q134393.png)
$$\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{\mathrm{k}} \:\left(\mathrm{k}!\right)^{\mathrm{2}} }{\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} \:\left(\mathrm{2k}\right)!}\:=? \\ $$