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**Homework Statement:**This is not a homework problem.

I am trying to imagine how Euler would have gone about getting the value of e, while he was trying to figure out the case of continuous compounding.

**Homework Equations:**I know how he reached up to the equation given below. I am not sure how that brilliant mind might have come to the conclusion that this looks like a constant.

$$ \lim_{n \rightarrow \infty} ~ ( 1 + \frac {1 }{N} )^N $$

Would he have calculated the output using different values of N and figured that it is progressing towards a limiting value as N increases?