Limit with factorial leads to familiar solution (contains errors)

Update: Thanks to those who have pointed out errors in this approach. One of them is kind of embarrassing to me. Read more here: https://math.stackexchange.com/questions/3896990/is-this-approach-to-the-limit-solution-kosher-lim-n-rightarrow-infty-frac?

This is a response to Dr. Peyam's video: https://youtu.be/ihrNrvoodq0 Try it on your own first. Then have a look at our solutions!

Read the blog version of this video: https://medium.com/mathadam/can-you-solvethis-limit-8a4ad44fafd ... https://www.youtube.com/watch?v=iL7NznqUV0s