Question

高数问题？

用比值审敛法怎么判断这道题的敛散性，谢谢！

Answer 1

级数是发散的，详情如图所示

Answer 2

lim a(n)/a(n+1)= lim (2^(n+1)+1) n!/[(2^n+1)(n+1)!]

=lim (1/(n+1)) *( 2* 2^(n) +2 -1 )/(2^n +1)
= lim 1/(n+1) *(2 -1/(2^n +1)) =0
所以发散