# Euler's method to compute the number Napier's constant

I am asking about the original way that Euler did to calculate Napier's constant, I heard that he was able to compute its first 23 decimals.

• I'm not sure how Euler did it, but a naive approach such as Maclaurin's series seems to converge reasonably quickly (there are faster methods such as Brothers' formula, but that's more modern). Still, 23 decimal places seems extremely tedious using the tools of his day: do you have a reference to support this? – Deepak May 23 '17 at 0:10
• @Deepak I actually read it in a website here is the link link – Hks.Adohkd May 23 '17 at 8:22

The article Napier's $e$ - $e$ in Leonhard Euler's Introductio says that Euler used the series $$e=1+{1\over 1}+{1^2\over 1\cdot 2}+{1^3\over 1\cdot 2\cdot 3}+\cdots$$ to obtain $$e \approx 2.71828182845904523536028\cdots$$
• To get an accuracy of $23$ d.p. (as per the OP), Euler would've had to compute the reciprocal of factorials up to $24!$, presumably by hand. That seems... unlikely. – Deepak May 23 '17 at 0:40