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Re: Math
Posted: 02 Dec 2009, 12:37
by Gota
Peet wrote:Counterexample - an=sin(n). L = limit of (Σai)/n as n goes to infinity = 0.
The limit of an as n goes to infinity does not exist, so it's not equal to L.
Thanks,thats a good counterexample.
Can you also show this in a general way using the definition of limit?
Re: Math
Posted: 02 Dec 2009, 12:38
by Gota
Peet wrote:Counterexample - an=sin(n). L = limit of (Σai)/n as n goes to infinity = 0.
The limit of an as n goes to infinity does not exist, so it's not equal to L.
Thanks,thats a good counterexample.
Can you also show this in a general way using the definition of limit?
Re: Math
Posted: 02 Dec 2009, 12:41
by Peet
It's been awhile since calc 151
Re: Math
Posted: 02 Dec 2009, 14:22
by koshi
You don't need the value of the partial sum limit, only it's existence. Showing that using anything near the raw defintion is foolish imo.