Question

is the sequence {sin((pi*n)/6)} bounded? monotonic? Convergant to a number < 1? bounded? or divergant?

Answer 1

It's divergent according to the test for divergence. the limit as n approaches infinity of (pi*n)/6 is infinity, and sin(infinity) is essentially anything from -1 to 1, but since we can't know, we just say it doesn't exist. Therefore, by the test for divergence, that sequence is divergent.