For all a > 0 and b > 1, the inequalities ln n n a ,

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For all a > 0 and b > 1, the inequalities ln n ≤ na, na n are true for n sufficiently large (this can be proved using L’Hˆopital’s Rule). Use this, together with the Direct Comparison Test, to determine whether the series converges or diverges.

n=1 (Inn) 100 1.1 n

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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