e vs pi

Originally posted by joe shmo
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?

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?

Generally when speaking of convergence one speaks of infinite sequences, series, etc.

Originally posted by joe shmo
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?

If it is a finite sum of finite terms then it is convergent. (Just add them up)

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.

Originally posted by amolv06
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.

if inf(S) = sup(S) when i -> infinity, then it is convergent, isn't it?
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)

I'm sorry, I'm not familiar with the notation.

Specifically, what are inf, and sup?

^^ Girlfriend left her account logged in -- sorry, it's confusing sharing a machine sometimes.