Question: For all a > 0 and b > 1, the inequalities ln n n a , n a n are true for n sufficiently

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.

00 2: n=1 n n 1 3n

00 2: n=1 n n 1 3n

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