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\displaystyle \lim_{n \to \infty} \dfrac{(2n+2)(2n+1)}{(n+1)^2} \div \left(\dfrac{n+1}{n}\right)^{2n} try again …

\text{let}\,\,\,a_n=\frac{(2n)!}{n^{2n}}\\\\\Rightarrow...

The ratio test seems to work for me.

Perfect!

After some hard work guys I found the best solution for that, just look...

Ratio tests are typically used for series with factorials because they cancel out nicely.

Try the ratio test?

After some hard work guys I found the best solution for that, just look...

d'alembert test also means ratio test, just look what a horrible limit we'll get using this test... :/

Try the ratio test?

Does the series converge or diverge? \sum_{n=1}^\infty\frac{(2n)!}{n^{2n}}\\\\\text{I tried to use d'alembert test but I got so hard...

After some hard work guys I found the best solution for that, just look...

After some hard work guys I found the best solution for that, just look...

You can, but you have to use a half-angle or double identity. Also, assuming you know the unit circle and radians...

Look up tangent of half angle.