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Calculus 101? I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e, was one of the first things learned in Calculus. I think we even briefly touched this in highschool.
To clarify this should not be 1/e, but e.
Calculus 101? I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e, was one of the first things learned in Calculus. I think we even briefly touched this in highschool.
> I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e To clarify this should not be 1/e, but e.
*without somehow wrapping around infinity http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%...
Here's my "e bookshelf" http://imgur.com/YBB33 , which uses the 1/n! definition. It only goes up to 1/3!, but ideally would approach 1/infinity!. e grows as the total area of the clear books on the left. For example, for the bottom shelf, 1/3! is the same as having all possible arrangements of three objects, and choosing one.
Earlier quoted context omitted.
> I recall that learning that lim(1 - 1/n)^n with n->inf is 1/e To clarify this should not be 1/e, but e.
It would be e if there had been a + sign in the parens, but with a - it is, in fact, 1/e. (1-1/n) is always less than 1; multiplying a bunch of factors less than 1 can't possibly* give you 2.something. *without somehow wrapping around infinity http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%...