求(2n)!/(n!)^2的收敛半径主要从!怎么化简

Question

求(2n)!/(n!)^2的收敛半径 主要从!怎么化简

Answer 1

an=(2n)!/(n!)^2
收敛半径
R=lim(n→无穷)|an/an+1|
=lim(n→无穷)|(2n)!/(n!)^2/(2n+2)!/(n+1)!^2|
=lim(n→无穷)|(n+1)^2/(2n+1)(2n+2)|
=1/4