# Limits with ChatGPT

By [Drasen](https://paragraph.com/@drasen) · 2023-03-10

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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 ](https://storage.googleapis.com/papyrus_images/407eee66a697802fdd7ae2eb0c58086f9c255c93acdec98ece6439f247ff437f.png)

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](https://storage.googleapis.com/papyrus_images/f2293ac80e57d17fe624c31c72417c3a7e140ce5952da392c662c894b4b532ba.png)

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

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*Originally published on [Drasen](https://paragraph.com/@drasen/limits-with-chatgpt)*