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 m 2 1 In m...

so that For m 1 sufficiently large say m k although in this case m 2 suffi ...

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.

m=2 1 In m