Does the series converge or diverge?
[math]\sum_{n=1}^\infty\frac{(2n)!}{n^{2n}}\\\\\text{I tried to use d'alembert test but I got so hard limit, so I thought about cauchy's test:}\\\\\lim_{n\to\infty}\sqrt[n]{\frac{(2n)!}{n^{2n}}}\\\\\text{Do u have any ideas how to calculate this limit?}[/math]
[math]\sum_{n=1}^\infty\frac{(2n)!}{n^{2n}}\\\\\text{I tried to use d'alembert test but I got so hard limit, so I thought about cauchy's test:}\\\\\lim_{n\to\infty}\sqrt[n]{\frac{(2n)!}{n^{2n}}}\\\\\text{Do u have any ideas how to calculate this limit?}[/math]