Here we examine the mathematical capability of ChatGPT *Q. find the limit of ((1+n)/e)^(-n)*n! as n goes to infinityconvert ((1+n)/e)^(-n)\*n! into [(e^n)/(1+(1/n))^n]\*n!, then substitute e for (1+(1/n))^nwith e^(n-1)\*n!, use Stirling's approximation to get e^n\*(n/e)^(n+1/2)\*sqrt(2\*pi/n), thus establish the limit goes to infinity