an/a(n+1)=n!e^n/n^(n+p)*(n+1)^(n+1+p)/[(n+1)!e^(n+1)]
=(1+1/n)^(n+p)/e=e^(nln(1+1/n)-1)(1+1/n)^p
=e^(-1/(2n)+小o(1/n))(1+p/n+小o(1/n))
=(1-1/(2n)+小o(1/n))(1+p/n+小o(1/n))
=1+(p-1/2)/n+大O(1/n^2),
由Raabe判别法知道p-1/2>1时,级数收敛,
p-1/23/2时级数收敛,p
an/a(n+1)=n!e^n/n^(n+p)*(n+1)^(n+1+p)/[(n+1)!e^(n+1)]
=(1+1/n)^(n+p)/e=e^(nln(1+1/n)-1)(1+1/n)^p
=e^(-1/(2n)+小o(1/n))(1+p/n+小o(1/n))
=(1-1/(2n)+小o(1/n))(1+p/n+小o(1/n))
=1+(p-1/2)/n+大O(1/n^2),
由Raabe判别法知道p-1/2>1时,级数收敛,
p-1/23/2时级数收敛,p