I know that ∑n=1 to infinity (sin(p/n)) diverges due using comparison test with pi/n, despite it approaching 0 as n approaches infinity.
However, an alternating series with (-1)^n*sin(pi/n) converges. Which does not make sense because it consists of two diverging functions.
Is there any intuitive explanation for this? Or is it just a rule that I need to remember when treating alternating series