Does anyone know where I can read Euler's original derivation of the infinite series used to define $e$?
I mean the series as defined in the wikipedia page about $e$.
Does anyone know where I can read Euler's original derivation of the infinite series used to define $e$?
I mean the series as defined in the wikipedia page about $e$.
It seems that Euler used the letter $e$ to represent the number $2.71828...$ in one of his earliest works, a manuscript entitled "Meditation upon Experiments made recently on the firing of Cannon," dated 1727 (published in 1862).
The first "published" $e$ by Euler seems to be in :
Jakob Bernoulli was the first to point out the connection between $\lim_{n \to \infty} (1 + 1/n)^n$ and the problem of continuous compound interest. By expanding the expression $(1 + 1/n)^n$ according to the binomial theorem (see this post), he showed that the limit must be between 2 and 3.
For $e^z = \lim_{n \to \infty} (1 + z/n)^n$, see Leonhard Euler, Introductio in analysin infinitorum : Tomus I (1748, new ed.1797), page 90.