a) absolutely convergent
b) conditionally convergent
c) divergent?
I know that
1
∫1/x^s dx is convergent <=> s<1 and
0
∞
∫1/x^s dx is convergent <=> s>1 but...
1
Note that if this obviously diverges, so we may assume WLOG that . So then notice that is positive, continuous, and non-increasing. Thus, we have by the integral test that the your integral shares convergence with so applying the root test we get ..soo