I am struggling with this one. For what values for p does the series converge?
I have tried the ratio test but I keep getting 1(inconclusive)
I am not sure by what you typed but it looks like you said its true for any p > 0 but when p=1 then and that is divergent. But when p = 2 or anything greater it looks like it is convergent. I need a way to show this. I think that if I can show that when p =2 that that is convergent than by comparison any p > 2 is convergent but that may be incorrect as well???
Here is one final way you could prove it, since your series is decreasing and positive after some value of N (use the inequality Ifirst gaave you to prove that) then your series covnerges iff
Now think what values of p does this serise converges...this time its pretty apparent.