A scientist models a damped oscillation by the alternating series
V=n=1∑∞(−1)n+1n3/2lnn.
Answer the following questions related to the model.
(a) Verify that the series V converges. Present a complete argument that addresses every required condition.
(b) The scientist wants the first N partial sums SN to approximate V with an absolute error less than 0.001. Determine the smallest integer N that guarantees this level of accuracy, and justify your answer.