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Re: Problem with limiits
*To*: mathgroup at smc.vnet.net
*Subject*: [mg65845] Re: Problem with limiits
*From*: Roger Bagula <rlbagulatftn at yahoo.com>
*Date*: Tue, 18 Apr 2006 06:56:40 -0400 (EDT)
*References*: <200604160544.BAA07913@smc.vnet.net> <e1vdsq$967$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Andrzej Kozlowski wrote:
>>
>
>
>
> For any sequence of real numbers a1,a2, a3 .... converging to a real
> number L, any infinite subsequence of it will converge to the same
> limit L. This is a very basic fact and is in fact true in any
> complete metric space (a subsequence of a convergent sequence is a
> Cauchy sequence, and therefore, in a complete metric space, is itself
> convergent.)
>
> Given the above, you only need the fact that there are infinitely
> many primes (proved by Euclid and before him by Eudoxus).
>
> Andrzej Kozlowski
>
What you are saying is that if I have a composite number c[m]
them the Limit:
Limit[(1+1/c[m])^c[m],m->Infinity]=E
as well.
What About:
Limit[(1-1/m)^m,m->Infinity] =1/E
Your reasoning gives:
Limit[(1-1/c[n])^c[n],n->Infinity]*Limit[(1+1/Prime[n])^Prime[n],N->Infinity]=1
and
Limit[(1-1/m)^m,m->Infinity]*Limit[(1+1/m)^m,m->Infinity]=1
This does give:
Limit[(1 - 1/m^2)^m, m -> Infinity]=1
Thanks for your help.
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