Re: analysis with limit.
- From: "mina_world" <mina_world@xxxxxxxxxxx>
- Date: Mon, 16 Oct 2006 10:27:55 +0900
"The World Wide Wade" <waderameyxiii@xxxxxxxxxxxxxxxxxxxx> wrote in message
news:waderameyxiii-5419B7.16465915102006@xxxxxxxxxxxxxxxxxxxxxxxxxxx
In article <egsro3$adj$1@xxxxxxxxxxxxxxxx>,
"mina_world" <mina_world@xxxxxxxxxxx> wrote:
hello sir~
if lim{n->00} n*(a_n) = 0,
show that lim{n->00} {1 + (1/n) + a_n}^n = e.
---------------------------------------------
um... i think...
i will use the L'Hospital rule.
When you use LHR, you usually learn very little. Taking the log
you get n*log{1 + (1/n) + a_n}. Recall log(1+h) = h + O(h^2)as h
-> 0. So the log of the nth term is n*[(1/n) + a_n] + n*O([(1/n)
+ a_n]^2), ...
yes...you already taught this method using Talyor' theorem to me ago.
so, i also have tried with this method.
but this also need the William Elliot' advice.
we need a diffferentiable extension function of a_n.
.
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