Example of absolute convergent series divergent

Question

I have learnt that in complete norm space any series that is absolute convergent is convergent.

However, I am wondering is there any example of divergent series which is absolute convergent in that norm space.

Thanks

Then you have learned something that is NOT true. The set of all real numbers is a complete normed space. The sequence {3, -3, 3, -3, 3, ..,} — user247327, Jan 23 '16 at 20:48

score -1 · Answer 1 · answered Jan 23 '16 at 20:52

-1

You said it yourself, if a series converges absolutely then the series converges. So you cannot have a divergent series that converges absolutely.

answered Jan 23 '16 at 20:52

fosho

Actually, this is not true if the space in question is non-complete. – mrf Jan 23 '16 at 20:59

1 Answers1