Question

求∑n^n/(n!)^2的敛散性.

Answer 1

简单分析一下即可，详情如图所示

Answer 2

收敛.
比值判别法.
u(n+1)/u(n)={(n+1)^(n+1)/[(n+1)!]^2}/[n^n/(n!)^2]=[(n+1)^(n+1)/n^n]/(n+1)^2=[(n+1)/n]^n/(n+1)=e/(n+1)=0