Chapter 7: Q. 5 (page 652)
A series can fail two of the three conditions, (i), (ii) and (iii), and still converge. Which of the three conditions must an alternating series pass in order to converge?
Short Answer
According to the Divergence Test if the sequence {ak} does not converge to zero, then the
series , diverges.
Hence, for the series, to be convergent it must pass the third condition.