Re: prove -1/2 is not a subsequential limit of S_n
- From: Torsten Hennig <Torsten.Hennig@xxxxxxxxxxxxxx>
- Date: Mon, 13 Oct 2008 02:46:43 EDT
Here is the problem...
S_n = -1 + (n+1)/2 cos((pi*n)/2)
prove -1 is not a subsequential limit of S_n
I am not sure where to start.
Is it enough to consider various values for n
and then show that of the resulting subsequences -1/2
is not a limit of
any of them?
That seems a little weird to me since we are not
proving that we are
examining all possible subsequences. Actually, is
that even possible?
Aren't there an infinitude of subsequences of an
infinite sequence?
Clearly, I am confused and would appreciate any
advice in how to tackle
this one.
Write down explicitely
S_0, S_1, S_2 and S_3.
From there, conclude the general form ofS_(4*k), S_(4*k+1), S_(4*k+2) and S_(4*k+3)
for k = 0,1,2,...
and analyze their convergence behaviour.
Best wishes
Torsten.
.
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