Consider the series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞an where an=(−1)nnna_n = \frac{(-1)^n}{\sqrt[n]{n}}an=nn(−1)n. What is the behavior of this series?
Converges absolutely.
Converges conditionally.
Diverges by the Test for Divergence.
Diverges because the sequence is not monotonic.