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.

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 $$ e \approx 2.71828182845904523536028\cdots $$

Wikipedia#cite_note-28) cites Euler's original text, which confirms the story:

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