How to prove it?

Hello, this question is not documented, because the definition of the function of e to the power of x is based on your formula, that is to say, Euler found a number (that is, e) that satisfies the above formula, so he gave this number a name and calculated it to be about 2.728. If you have to prove it, it only proves that there is a limit -e in the variant of the formula you said. The specific process is as follows:

Through average inequality, there are

That is, the order

Monotonic rise; On the other hand, we try to prove.

. direct proofs

, obtained from the average inequality.

Obviously there is.

, so

Established, so

Established.

therefore

There is an upper limit for monotonic rise, that is

Convergence.

(The original proposer of the above certificate is German leonhard euler)