- #1
musicgold
- 304
- 19
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?
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?