Proving Convergence of Series in a Given Norm

[Somefantastik]

Given a sequence, how does one prove that the associated series in convergent or not, in a given norm? For example,

$$\sum_{k=0}^{\infty}a_{k}$$ in $$||\cdot||$$

The process to do this is not in my book; I'm told how to determine whether a series is cauchy, but I'm not sure how to use that to show it's convergent.

 

[dacruick]

depending on the series there will be a different method for proof of convergence or divergence. is there a specific series you are speaking of?

 

[Somefantastik]

I have several, in several spaces.

$$f_{n}(t) \ in \ (C[0,1],||\cdot||_{\infty})$$

is an example of one.

 

[dacruick]

got nothing for you man. sorry.

 

[dacruick]

I don't even understand your notation. good luck though

 

[Somefantastik]

bump, can someone please give this another look? I'd like to work these problems, but my book is not helpful and my campus is closed this week :(

If there is no help, can a moderator move this post into the Homework Help Forum?