Given an alternating sequence.
The Absolute Value Theorem states that: If the limit of the absolute value of the sequence is 0 then the limit of the original sequence is also 0.
However if, the limit of the absolute value of the sequence is not 0 (some value) then there is "no conclusion".
But wouldn't that just imply that the sequence would alternate between this value making the limit DNE and therefore the sequence divergent? Or is this only for all cases where the sequence is in fact alternating.