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Limits with ChatGPT

Here we examine the mathematical capability of ChatGPT

*Q. find the limit of ((1+n)/e)^(-n)*n! as n goes to infinity

convert ((1+n)/e)^(-n)\*n! into [(e^n)/(1+(1/n))^n]\*n!, then substitute e for (1+(1/n))^n
convert ((1+n)/e)^(-n)\*n! into [(e^n)/(1+(1/n))^n]\*n!, then substitute e for (1+(1/n))^n
with 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
with 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