(7) Consider the sequence (a.) given by 1 n In(n) In(In(n)) (a) Show that a ≤ for all integer n ≥ 3, where k R is some f

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7 Consider The Sequence A Given By 1 N In N In In N A Show That A For All Integer N 3 Where K R Is Some F 1 (15.45 KiB) Viewed 29 times

(7) Consider the sequence (a.) given by 1 n In(n) In(In(n)) (a) Show that a ≤ for all integer n ≥ 3, where k R is some fixed constant. [4 marks] Hint: You may use the fact that In(x) 21 1-1/ X for all a>0, without proof. (b) Evaluate the limit of (a), if it exists. [2 marks] (e) Apply the integral test to decide whether the series On converges or diverges. [8 marks] iM8 Σ =3