Determine the convergence of ∑n=1∞cos(n)n\sum_{n=1}^{\infty} \frac{\cos(n)}{n}∑n=1∞ncos(n). Which statement is correct?
Diverges because cos(n)\cos(n)cos(n) oscillates and ∑1n\sum \frac{1}{n}∑n1 diverges
Converges absolutely by comparison to ∑1n2\sum \frac{1}{n^2}∑n21
Converges by Dirichlet's Test (bounded partial sums of ∑cos(n)\sum \cos(n)∑cos(n)) but does NOT converge absolutely
By Root Test with L=1L = 1L=1; inconclusive