Question

I have a question about series and sequences - so I understand that IF a series converges, then the limit goes to zero. However, if the limit goes to zero, the series could still diverge. How does this make sense if there is a theorem that states that if the limit of partial sums is a finite existing number (couldn't that be zero?) than the series is also convergent.

Answer 1

You must distinguish carefully between SEQUENCE and SERIES.

If a SERIES converges, the related SEQUENCE must have a limit of zero.

A Sequence is just a list, possibly a very large list.
A Series is the sum of the elements in the list.

Answer 2

ok, thanks!