Question Number 204558 by universe last updated on 22/Feb/24
![lim_(nāā) n^(ā3/2) [(n+1)^((n+1)) (n+2)^((n+2)) ...(2n)^(2n) ]^(1/n^2 ) = ?](https://www.tinkutara.com/question/Q204558.png)
$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}^{ā\mathrm{3}/\mathrm{2}} \left[\left(\mathrm{n}+\mathrm{1}\right)^{\left(\mathrm{n}+\mathrm{1}\right)} \left(\mathrm{n}+\mathrm{2}\right)^{\left(\mathrm{n}+\mathrm{2}\right)} …\left(\mathrm{2n}\right)^{\mathrm{2n}} \right]^{\mathrm{1}/\mathrm{n}^{\mathrm{2}} } \:=\:? \\ $$