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I was thinking alternating series test, but cant that only be used for testing for convergence, not for testing divergence?
The divergence test doesnt work for indeterminant forms.Hurkyl said:How about the divergence test? :tongue2:
LeonhardEuler said:You'll have to be more specific. The convergence of what? The sequence of terms, [itex] a_n=i^n[/itex], the series, [itex]\sum_{n=0}^{\infty}i^n[/itex], or some sequence or series that just has [itex]i^n[/itex] as one term? I can tell you right now, the first two diverge.
[itex]i^n[/itex] is not an indeterminant form.Agnostic said:The divergence test doesnt work for indeterminant forms.
There isn't an indeterminant form involved. :tongue2:The divergence test doesnt work for indeterminant forms.
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.
Right, exactly!Agnostic said:The limit of [itex]i^n[/itex] as n goes to infinity doesnt have a solution does it?
No, they alternate ... i,-1,-i,1,i,-1,...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?
But that is not the same as saying indeterminant form?LeonhardEuler said:Right, exactly!
So the limit doesn't exist. Then can it equal zero?Agnostic said:No, they alternate ... i,-1,-i,1,i,-1,...
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?
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.But that is not the same as saying indeterminant form?