Determine the convergence of ∑n=1∞cos(n)n3/2\sum_{n=1}^{\infty} \frac{\cos(n)}{n^{3/2}}∑n=1∞n3/2cos(n)
Converges absolutely by comparison with ∑1n3/2\sum \frac{1}{n^{3/2}}∑n3/21
Converges conditionally because cos(n)\cos(n)cos(n) oscillates
Diverges because cos(n)\cos(n)cos(n) is bounded away from 0
Convergence cannot be determined without the Dirichlet Test