Simple problem involving comparison test for series...

I have a simple question involving the comparison test for series. I keep getting that it diverges, but the book says it diverges and I'm not getting why that is. The problem asks whether the series from n=1 to infinity converges. The expression is [cos(n*pi)]/[n^(3/4)]. My reasoning is that the numerator, the cos(n*pi) is always equal to or greater to 1, so it could be compared to 1/n^(3/4), which is a p-series with p=3/4, so it diverges. Therefore, the original expression diverges as well since it is smaller than the one it was compared to. But that's not right. What should I compare it to? I now notice that the cos(n*pi) can be negative, but how does that affect the problem? Please help; thanks.