Which of the following series is not absolutely convergent?

Question

Which of the following series is not absolutely convergent?

A
B
C
D

Answer 1

A series ∑_{(n=1 to ∞)} a_n converges absolutely if ∑ l a_n l converges.

So, inserting absolute value symbols appropriately, A converges absolutely by the Geometric Series Test, and choices C and D converge absolutely as they both become p-series with p = 2 and 4 respectively.