This is what I'm studying, but at the same its a question that I'd like to know out of curiosity.
When discussing convergence/divergence of trigonometric functions, what rules are the most important to guide myself with?
For instance take
$$\sum_{n=1}^{\infty} \cos(\frac{\pi n}{2})$$
This seems to diverge, due to the 4 different possible inputs. So it never really converges to a single value because it oscillates in this sense. So first question, is my intuition here correct?
$$\sum_{n=1}^{\infty} \frac {\sin(\frac{\pi n}{2})}{\cos(\frac{\pi n}{2})}$$
This tan function, I would say it does not converge because it is two oscillating functions which do not have the same value, meaning it will never simplify out. Is once again my intuition correct? Is the key when looking for the convergence or divergence of these trigonometric series to pay attention to the oscillation of the component functions and seeing if they possibly produce some sort of constant.
Thanks for your time!