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Originally posted by joe shmoThen again, this single term could be evaluated at a point other than pi, ie (pi+22) ect...how do we get around this logically? Or by the definition does the existance of any finite sum imply convergence?
just for clarification when I stated the series doesn't converge I thought of it in the way almov did, but because ( as fabian pointed out ) it is a series of only one term im going with fabian, if terms were separated by commas It doesn't converge.
On a side note: It does leave me confused? Does the sum continue in a non-distinct way?
Originally posted by joe shmoIf it is a finite sum of finite terms then it is convergent. (Just add them up)
Then again, this single term could be evaluated at a point other than pi, ie (pi+22) ect...how do we get around this logically? Or by the definition does the existance of any finite sum imply convergence?
Originally posted by amolv06if inf(S) = sup(S) when i -> infinity, then it is convergent, isn't it?
So I guess the question is, are finite sequences and series said to converge? I wouldn't think so, but I'm not sure about this.
Then it must follow that inf(S) = sup(S) when i -> n also is convergent, right?
In math classes we mostly deal with the hard stuff, and the hard stuff is here when i -> infinity. When when i -> n, then the answer is trivial, i.e. not very hard stuff, therefore we seldom deal with this.
(n is the max number of terms in a series)