1. The problem statement, all variables and given/known data The problem is divided into two sections: a) does the improper integral: 2ln(x)/x^7 (from 1 to infinity) Converge or diverge? If it converges, to what value? b) Determine whether the series: sigma n=1 to infinity (2ln(n)/n^7) converges or diverges. 2. Relevant equations Integration by parts? 3. The attempt at a solution For the first part, I made the limit as c--> infinity, and took out the 2, then I simply integrated by parts where: u = ln(x) du= 1/x dx dv= x^7 dx v = (x^8)/8 and ended up with: I = 1/4 lim c--> inf (x^8*ln(x) + (x^8)/8) from 1 to c When I work it out, I get it Diverges, as the end result is infinity... But it's supposed to converge... As for the second part, I assumed that they were similar where I could use the integral series test (ending up with the same result as the first part) to get the answer, but again, the answer lead to convergence.... Am I using the correct techniques? Thanks!