Calculs

(2n -1) n sin 2 (25) 2. Let a, = for n 21. 2n a. Write out the first 6 terms of the sequence ( a, through a ), all with simplified fractions. b. Determine lima . Note: You must show all your work and justify your steps carefully. C. Prove a, converges conditionally, but not absolutely. Note: You must show all your work 1=1 and justify your steps carefully. d. For the series in part (c), what value of n must your use to compute the n partial sum, S, , so that S, is accurate to within 0.005? You do NOT need to calculate S ; just tell me what n works. Show all work