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- Thread starter Agnostic
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Hurkyl

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How about the divergence test? :tongue2:

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LeonhardEuler

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Hurkyl said:How about the divergence test? :tongue2:

The divergence test doesnt work for indeterminant forms.

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LeonhardEuler said:

I must prove that [itex]\sum_{n=0}^{\infty}i^n[/itex] diverges.

Or rather, I must prove wheter or not its convergent of divergent. I know its divergent, but I still have to prove it.

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LeonhardEuler

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[itex]i^n[/itex] is not an indeterminant form.Agnostic said:The divergence test doesnt work for indeterminant forms.

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Hurkyl

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The divergence test doesnt work for indeterminant forms.

There isn't an indeterminant form involved. :tongue2:

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LeonhardEuler

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Oh, that's simple. Use the divergence test as Hurkyl suggested. Do the terms in the series approach zero as n approaches infinty?Agnostic said:I must prove that [itex]\sum_{n=0}^{\infty}i^n[/itex] diverges.

Or rather, I must prove wheter or not its convergent of divergent. I know its divergent, but I still have to prove it.

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The limit of [itex]i^n[/itex] as n goes to infinity doesnt have a solution does it?

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LeonhardEuler

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Right, exactly!Agnostic said:The limit of [itex]i^n[/itex] as n goes to infinity doesnt have a solution does it?

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LeonhardEuler said:Oh, that's simple. Use the divergence test as Hurkyl suggested. Do the terms in the series approach zero as n approaches infinty?

No, they alternate ... i,-1,-i,1,i,-1,...

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LeonhardEuler said:Right, exactly!

But that is not the same as saying indeterminant form?

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LeonhardEuler

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So the limit doesn't exist. Then can it equal zero?Agnostic said:No, they alternate ... i,-1,-i,1,i,-1,...

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LeonhardEuler

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No, an indeterminant form is something like [itex]\frac{0}{0}[/itex], or [itex]\frac{\infty}{\infty}[/itex], or [itex]1^{\infty}[/itex]. A non-existant limit is just a non-existant limit.Agnostic said:But that is not the same as saying indeterminant form?

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Hurkyl

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But that is not the same as saying indeterminant form?

An indeterminate form is a "limit form" for which we don't have enough information to say what the limit really is, or if it exists. For example, [itex]\lim_{x \rightarrow 0} x/x[/itex] has the indeterminate form 0/0.

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Its usually always silly mistakes :D

Thanks alot guys..

Thanks alot guys..

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