MATH08058 Calculus and its Applications (7) Consider the sequence {an)3 given by 1. = an n In(n) In (In(n)) (a) Show tha

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Math08058 Calculus And Its Applications 7 Consider The Sequence An 3 Given By 1 An N In N In In N A Show Tha 1 (26.91 KiB) Viewed 44 times

MATH08058 Calculus and its Applications (7) Consider the sequence {an)3 given by 1. = an n In(n) In (In(n)) (a) Show that an for all integer n 23, where ke R is some fixed constant. [4 marks] In(r) 21. Hint: You may use the fact that for all r> 0, without proof. (b) Evaluate the limit of {an), if it exists. (c) Apply the integral test to decide whether the series Σ an n=3 converges or diverges. [2 marks] [8 marks]