Is it okay to apply divergence test on a series $\sum a_n$ and show that this series diverges by showing that $|a_n| = \infty$?
If I have alternating sequence of $(-1^n) n^2$, can I say absolute value of this, $n^2$ goes to infinity therefore its series diverges by Divergence Test?
The definition of divergence test only mentions I must show divergence of the sequence, not the absolute value of sequence. I guess a better way of putting this question is to ask does divergence of absolute value of a sequence imply the divergence of the original sequence?
Thanks in advance!