Math

[Gota]

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?

[Gota]

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?

[Peet]

It's been awhile since calc 151

[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.