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I just saw a video of 3Blue1Brown on derivatives of exponentials functions and now I understand better where does the Euler's number comes from. But i still don't understand why Jacob Bernoulli's compound interest problem limit's is equal to e ?

I'm talking about this limit: $$ e = \lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}$$

re-edit: Here, e is defined as the sum of the infinite series: $${\displaystyle e=\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+\cdots ,}$$ where n! is the factorial of n.

I don't want a proof, but an intuition on why e appears in Jacob Bernoulli's compound interest, if that makes sense.

Dimuel Tripotin
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    For this to be a well-posed question, you need to start with a definition of $e$. Many people use this limit as the definition, after all. – lulu Oct 03 '23 at 17:21
  • Whatever definition you had in mind, I expect that this is a duplicate. – lulu Oct 03 '23 at 17:22
  • It is worth asking why we expect that limit to exist in the first place, but asking why it is $e$ is basically a matter of which definition you use. – whpowell96 Oct 03 '23 at 18:14

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