Question

Does the series converge or diverge?

Sum (n*cos(1/n))/(sqrt(n^5-1)), n->1 to infinity.

Answer 1

first note that cos(1/n) is always between -1 and 1. then we see that our bn = (n*1)/(n^(5/2)) which is always going to be bigger then the original series. bn then simplifies down to 1/(n^(3/2)), which is a p series where 3/2 is bigger then 1 and therefore convergent thus by basic comparison test the original series converges

Answer 2

Thanks!