http://www.17centurymaths.com/contents/introductiontoanalysisvol1.htm
The chapter $7$ of this mentions a proof of expansion of $e^x$ without using idea of derivative but only using idea of infinitesimals. Everything that Euler did was beautiful but I am unable to convince me at this point of the proof,
Euler sets
$j/j=1$,
$(j-1)/j =1$,
$(j-2)/j =1$,
$\quad\vdots$
as the value of $j$ is infinite. But my question is how long is this true? I mean as the value of $n$ goes to infinity in $(j-n)/j$ will it still be converging to $1$?
It’s clear that it approches $0$. So why did Euler said it's $1$ (its not exactly mentioned by Euler but the information in the para explains this thing).
If possible please explain me that part in an elaborated way as an answer. And please explain me step by step as I am a bit confused regarding it.