N 2 a n n 21 n lnn using the integral test let f x 1

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1.n=2|an|=n=21nlnn1
2. Using the alternating series test onn=2an=n=2(-1)nnlnnwherebn=1nlnn:(i)bnis decreasing for alln2 (asf(x), above, is decreasing).(ii)limn→∞bn= limn→∞1nlnn= 0n=2anconverges conditionally sincen=2anconverges by thealternating series test andn=2|an|diverges.Grade:2424

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