lim (n ---> +oo) xn = e^1 = e
hope it' ll help !!
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CogitoErgoCogitoSum say: Well, what do you mean not 1? Its pretty easy to prove that the limit converges. Its also pretty easy to bound the limit, to show that the limit is larger than 2 but less than 3. Why does it equal e? Thats the definition of e. Its no coincidence, that is the limit that Bernoulli studied when he defined the constant e. Its nonsense to ask why something equals that which defines it. You should have been taught that this limit is the *definition* of e.
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What do you mean assume that 1 is a really big number? Dont say 1/n is 0 or 1^infinity = 1 because these are nonsense statements and prove to me that you dont understand basic limits or indeterminate forms. Something that should have already been explained thoroughly to you.
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Dixon say: As you point out, 1/n isn't zero, it tends to zero but it is always finite. And when you raise (1 + not quite zero) to a power that also tends to infinity, that is an awful lot multiplication to make it a bit more than one.
I suspect that if you do the binomial expansion of (1 + 1/n)^n for a few terms (keeping it in terms of n), it will simplify to the Taylor series equivalent of e^x with x = 1, which is basically the sum of the reciprocal factorials.
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Alexander say: 1^{inf}
log(1^{inf}) = inf*log(1) = inf*0
-- haw many to be?
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