For all a 0 and b 1, the inequalities ln n n a , n a n are true for n sufficiently large (this can be proved using LHopitals Rule) Use this, together with the Direct Comparison Test, to determine whether the series converges or diverges n 1 (Inn) 100 1 1 n...

Then But 00 nN Choose N so that Inn 00005 for n N Then also for n ...

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

Question:

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