Researching on the internet, it is easy to find that Bernoulli was the first to give a one-digit approximation for $e$ (specifically, $2.5<e<3$). But, I cannot find any source describing exactly how he gave this approximation.
Some websites say he used a "power series" argument, but I cannot find this argument anywhere. A comment at the bottom of Bernoulli's Wikipedia article directs to Bernoulli's original paper (see the link below), but it is in Latin and the notation is not understandable to me.
https://books.google.com/books?id=s4pw4GyHTRcC&pg=PA222#v=onepage&q&f=false
Does anyone know of a source that has this original proof? Thank you for any help!
Best Answer
Long comment
In the paper linked (1690 - see also : The number e ) Jacob Bernoulli is trying to solve the
In the latin text he is considering a sum $a$ with interest (usura annua) $b$, arriving at the following approximation :
Then he put $a=b$ and the result is :
If we put $a=1$ we finally have :
But Bernoulii does not call it e :