one other technique that would work is an interesting criterion involving the partial sums. let sn be the nth partial sum of the series. If for every epsilon greater than zero there exists an N such that for all n>N we have
|sn+k - sn|<epsilon for all k >= 1, then the series must converge...
Dirichlet's test will work for this series.
we can think of sin(n)/n as the product sin(n)*1/n.
dirichlet's test says that if one of the sequences in the product is bounded, and the other is monotone and converges to 0 then the series of the product of sequences must converge.
the sequence...